After buying a home in Barrington Hills, Chaoshan Lai and his wife couldn’t unload the 15-year-old townhouse that they’d bought for $935,000 in Central Station, a taxpayer-subsidized development in the South Loop where former Mayor Richard M. Daley lived for years.

Lai couldn’t even find anyone to rent the townhouse on South Prairie Avenue — until he got a call in 2013 about a woman who’d gotten a “housing choice voucher,” from the Chicago Housing Authority through a program that had long been called Section 8.

Lai says the woman wanted to lease his three-bedroom, three-and-a-half bath home, which has a library and is within walking distance of Soldier Field and the lakefront.

“I said, ‘You probably cannot afford the rent,’ ” Lai recalls. “But they said they have a special program in the ‘opportunity area’ that pays much better. I said, ‘Let’s give it a shot.’ ”

It ended up being a good deal for Lai. Since June 1, 2013, he’s collected more than $100,000 from the CHA, which administers public housing in Chicago for the U.S. Department of Housing and Urban Development. The CHA pays him $3,911 a month in federal funds to lease his townhouse to the woman and three others in her household, including a child under the age of 6, records show.

It also has been a good deal for Lai’s tenant. She pays no rent because, CHA officials say, she has no income. The CHA declined to identify her or other voucher clients, though it released the names of landlords.

Public housing doesn’t conjure images of a near-$1 million home. But the CHA foots most or all of the bill for Lai’s tenant and others to live in luxurious homes, even as tens of thousands of other low-income Chicagoans remain concentrated in poor, segregated areas or stuck on waiting lists to get housing assistance.

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That’s one of the key findings of a Chicago Sun-Times / Better Government Association investigation that will, over the coming months, examine the effects of the city’s massive “Plan for Transformation” — one of the most ambitious efforts nationwide to shift low-income residents out of crime-ridden, high-rise public housing projects like Cabrini-Green and the Robert Taylor Homes.

As one of the main elements of that effort, the CHA is providing housing vouchers to more than 107,000 people in nearly 45,000 households in Chicago, most of them African-American. The vouchers give them a financial hand to lease apartments and homes from private landlords in any neighborhood they choose.

It’s an expensive effort, costing more than $47 million a month, with the federal government picking up $35.9 million of that and CHA tenants paying the rest.

But the program is riddled with inequities, the Sun-Times and BGA found. Among them:

• The CHA pays for some to live in high-rent, luxury properties, largely in upscale neighborhoods that are predominantly white. Many of them contribute little or nothing toward their rent. On the other hand, thousands pay far more and remain clustered in poor, black neighborhoods on the South Side and the West Side.

• The amount of financial assistance that voucher-holders get varies widely, largely because of the CHA’s willingness to provide more help to people who find homes in “opportunity areas” that traditionally haven’t welcomed public housing tenants.

• Of those receiving a voucher, 298 are leasing apartments, townhouses and single-family homes that cost $2,000 or more a month. The CHA spends a total of $7.5 million a year on those units, ranging from spacious homes to condos in skyscrapers.

• Taxpayers cover a higher percentage of the total rent for voucher-holders in two downtown wards than anywhere else: 87 percent in the 42nd Ward and 83 percent in the 2nd Ward.

Meanwhile, about 50,000 households remain on waiting lists to get one of the coveted vouchers, agency records show — more than the number who have vouchers.

Eighty-eight percent of households in the voucher program are headed by an African-American, most often a woman.

The CHA says it doesn’t tell the people with housing vouchers where to live. They’re free to find any place they can to rent, though the CHA has to inspect and approve it.

One of the more controversial parts of the voucher program has involved the effort to let people know they can move to opportunity areas, away from the old public housing clusters.

Opportunity areas are part of the Plan for Transformation, which, under Mayor Daley, saw housing projects demolished and the number of the federally funded housing vouchers rise.

The CHA currently has 4,690 households, with a total of 9,841 people, living in opportunity areas with the help of vouchers.

Over the past five years, the CHA has been willing to pay a premium — up to triple its standard rent payments — for apartments, condos and houses in these areas. There are now 1,332 households with a total of 3,584 people benefiting from that added financial help.

The most extravagant of the rent deals will end when their leases run out within the next two years, according to the CHA. It began scaling back on paying such high rents in 2014 in response to news stories and after discussions with HUD.

The opportunity-area program will continue. But voucher-holders are going to have to find less-expensive homes to stay in those areas, which include Lincoln Park and the Loop, because the CHA will pay only one-and-a-half times its normal top rents, rather than triple, to help poor people live there.

“We figured we do need to balance the obligations and the fiscal responsibilities we have with the need to provide people with access to the opportunity areas, which is an important part of moving people up the economic ladder,” says Molly Sullivan, a spokeswoman for the CHA.

CLICK HERE FOR PHOTOS AND DETAILS OF CHA’S LUXURY GAP

CHA officials say they don’t have a set budget for vouchers in the opportunity areas. They say the agency provides information on opportunity areas to everyone who gets a voucher, then offers additional counseling to those who want it.

Some people want to live in neighborhoods like Englewood because they have ties there, says Eugene Jones Jr., the CHA’s chief executive officer, while others would prefer a high-rise downtown.

“Your choice may be different from someone else’s choice,” Jones says. “We find a lot of people want to stay where they’re comfortable.”

CHA records show 97 percent of voucher-holders live in homes where the rent is between $500 and $1,500 a month. Most of them pay part of their rent based on their income — unlike Lai’s tenant and others who pay little or nothing to live at a swanky address.

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Jamaine Parish and the 14 other people in his household, for example, live in a 1,200-square-foot bungalow in Marquette Park on the city’s Southwest Side. The home, where they moved in December, has seven bedrooms, including two in the basement.

CHA records show Parish has the largest household in the voucher program. He and his wife have seven children. His grandmother and her adopted and foster children also live with them.

Their rent is $1,938 a month. Parish, who’s a tax preparer, pays a quarter of that — $479. The CHA picks up the rest.

Parish says that although the home on South Artesian isn’t ideal for his huge family, it’s an improvement from the greystone at 37th Street and Indiana where they lived for two years using a voucher.

“Sometimes, you just have to do what you have to do to make it work,” says Parish, who waited more than six years to get one of the coveted vouchers.

Parish pays more in rent than 84 percent of the households in the voucher program. His share is higher than what some one-person voucher households pay to live in high-rises downtown.

“Wow,” Parish says. “Think about how many people are residing there and how many are residing here.”

WHERE HOUSING VOUCHER-HOLDERS LIVE: Click on map below, then arrows at left to see your ward.

The Sun-Times and BGA also found:

• 13 percent of the households in the voucher program citywide — 5,778 — pay no rent, with the CHA picking up the entire tab. That’s because they have no income or their income — from foster-care payments, for instance — doesn’t count toward their rent under HUD rules.

• 467 voucher-holders each pay $1,000 a month or more toward their rents — including a woman whose rent is $2,966 a month for a 32nd-floor condo in the Loop. She pays $2,002 of that. Taxpayers cover the remaining $964. A check of local rental listings shows there are many one- to three-bedroom apartments available for up to $2,000 a month, including some in opportunity areas.

• 18,157 vouchers are held by one-person households — and at least 1,450 of them pay no rent, including a man who lives on the 15th floor of a Loop high-rise where the $2,260-a-month rent is covered by taxpayers.

• 187 big apartment buildings — some set aside for seniors — have at least 10 voucher-holders. Altogether, those buildings — many of them in Uptown or Edgewater or on the South Side — have 7,542 residents living there with the help of vouchers. A dozen have more than 100 residents living with vouchers.

• The two cheapest apartments in the voucher program — going for just $340 a month — are on North Winthrop in Uptown. One of the single men with a voucher who lives there pays $241 of the cost himself. Another pays $212. Both pay more than some voucher-holders do for high-priced condos downtown.

• Just down the block, 150 voucher-holders — all one-person households — live in a building where rents are $642 to $674 a month. Some pay the entire cost. Both Winthrop buildings are managed by Mercy Housing Lakefront, a not-for-profit agency that provides affordable housing.

To get a voucher, the federal government requires people to meet income guidelines based on household size. To qualify, a single person in Chicago has to make $42,600 or less a year — 80 percent of the area’s median income. A family of four can’t make more than $60,800.

People can use a voucher to lease any house, condo or apartment in the city or elsewhere that meets the rent guidelines set by the CHA, which range from $784 a month for a studio apartment to $2,775 a month for an eight-bedroom home.

The CHA shares the cost of the rent with tenants, who generally are required to pay as much as 30 percent of their income, or at least $75 a month in rent.

Chicago landlords are required, by city ordinance, to accept housing vouchers as payment as long as the full rent gets covered by the CHA and the tenant.

“When folks come to us — they’ve found a unit in a certain building, and they want to rent there — as long as it passes our inspection and we can agree on a reasonable rent with that landlord, we can’t turn that down,” says Katie Ludwig, who oversees the voucher program for the CHA.

People have gotten some rich deals as a result of that:

• A single woman is leasing a two-bedroom condominium just north of Trump Tower for $3,000 a month. She pays $248, and taxpayers pay the rest — $2,752.

• A woman, her teenage son and a daughter who’s away at college have a two-bedroom condo in a South Loop high-rise with sweeping views of Lake Michigan for $3,020 a month. She pays $143; taxpayers pay $2,877.

• On North Harbor Drive near Navy Pier, a woman and two other people live on the 45th floor in a three-bedroom condo where the rent is $3,780. She pays $201; taxpayers pick up the remaining $3,579. Another three-bedroom condo in the same building, on the 37th floor, is leased to a woman and four others who pay no rent, with taxpayers covering the entire $3,770-a-month tab.

There are costly deals elsewhere in the city, too.

The CHA’s most-expensive lease is $4,800 a month. That’s for a five-bedroom home on Ohio Street near Ashland Avenue. A family of nine leases the home from Glenn Kahn, an attorney who used to live there and who collects $283 a month in rent from the family and the remaining $4,517 from taxpayers.

The housing authority, whose board is appointed by the mayor, pays the entire rent for two five-bedroom houses in Bridgeport, in the shadow of the shuttered Fisk power plant — $3,000 a month for each house. Five people live in one of the houses. The other is occupied by Linda Turpin, 65, and her two adult daughters, one in college, the other unemployed.

Turpin’s grandchildren went to school with the children of her landlord, Manuel Cuzco, who purchased the home 10 years ago for $404,000, records show.

Turpin moved in two years ago after living in a South Side home where she says her windows got shot out. Now, she’s next door to a retired Chicago cop she says looks out for her.

“When I came here, I felt special,” Turpin says. “It has a little back yard. I don’t have to barricade myself in this house. I get to live like a human being.”

Turpin is among the people who will be moving out of her home soon because the CHA has slashed in half the amount it will spend on rents in the opportunity areas.

“There may be some landlords who might take less rent,” says Ludwig. “There might be some folks who might be able to afford a little bit extra. For the most part, a lot of people are likely going to have to move. And we’re working with them. ”

Turpin, who says she has several health problems, says Cuzco won’t cut the rent to about $1,700 a month — the amount the CHA would pay under its new rules. She says her lease ends in December. She doesn’t know where she’ll end up.

“Where would I go? I have no idea,” Turpin says. “I’m really afraid.”

Tim Novak, Chris Fusco and Mick Dumke are Sun-Times reporters. Brett Chase is a Better Government Association investigator.

Contributing: Data Reporting Lab editor Darnell Little