Is the James R. Thompson Center a postmodern architectural gem — or a cockroach-infested dump where office wastebaskets do double-duty catching rainwater from the leaky ceiling?

A group of three — an architect, real estate reporter and an architectural historian — have launched the James R. Thompson Center Historical Society “to encourage all to visit the building and contribute to the ongoing discussion of its past, present, and future in Chicago.”

The building at 100 W. Randolph St. has long been a love-it-or-hate it part of Chicago history.

And Gov. J.B. Pritzker is not on Team Love It.

The governor is trying to sell it.

While the building — designed by Helmut Jahn in 1985 — is lauded for its innovative structure, it has long been criticized by state employees for its state of disrepair, including temperature problems, leaky ceilings and cockroaches. There’s also a permanent odor seeping up to the 16th-floor offices of the governor and others from a lower level food court.

But the historical society — formed by Elizabeth Blasius, Jonathan Solomon, and AJ LaTrace — has a deep appreciation for the building, no matter what ends up happening to it.

LaTrace said the Thompson Center “was supposed to be a symbolic gesture.”

“It was supposed to be an optimistic building for the future. And it was a building that people could be proud of, and the state workers could be proud to work in,” LaTrace said. “And of course, we all know about the issues ... but the reality is it’s an incredibly ambitious building, and we think it’s worthy of not only continuing the discussions but it’s up there with the other notable Chicago landmarks.”

LaTrace — a blogger and real estate reporter — said the group simply wants Chicagoans to go see the building, which he said “belongs to the residents” as a state-owned property.

“What we’re trying to do is invite the public in,” LaTrace said.

The group makes its case on its website: “As a city known around the world for its contributions to architecture and design, Chicago also has an equally troubling history of discarding many of its most significant structures and public places. We ask a simple question: Do we dare squander Chicago’s great architectural heritage? Our city’s cultural heritage — and the Thompson Center itself — belongs to all Chicagoans.”

Their mission includes advocating for the “physical preservation of the building while fully recognizing and understanding that the sale and demolition of the JRTC is a possible outcome.”

They plan to hold an inaugural tour of the building’s public spaces on Oct. 17. A Halloween tour is also on tap — encouraging tour-goers to “bring your favorite ‘80s outfit or costume” for a walk through the building’s lower atrium.

In April, Pritzker signed a measure that will make it easier to sell the long criticized state building. The legislation was passed by the Illinois General Assembly in 2017 but was never sent to then-Gov. Bruce Rauner due to a procedural hold.

That measure provided for the sale of the Thompson Center by a “competitive sealed proposal process within two years.” The buyer must also enter into an agreement with the city and the Chicago Transit Authority to maintain operations of the Clark and Lake station, which is one of the most complex and busy CTA stations in the city.

Pritzker has said he wants to sell the building to use it as “an asset to offset liabilities, possibly liabilities in the pension system.”

The governor’s office put out a request for proposals on Aug. 28 to obtain project management and technical expertise about a sale of the historic building. Those proposals are due on Friday.

According to Pritzker’s office, the construction cost in 2016 was estimated to be more than $300 million to bring the building “into a good state of repair.” The operating expenses are also more than $17 million due to the building’s size.

In the event of a sale, employees at the Thompson Center — who have often complained about its underutilization and maintenance issues — will be moved to the Michael A. Bilandic building across the street, and “other under-utilized, state-owned or rented facilities,” the governor’s office said. About 2,200 state employees work in the building.

Last month, the governor’s office announced that Pritzker had paid $275,000 out of his own pocket for a governor’s office revamp in the building, including carpeting, paint and ceiling tile work “so that the space would no longer be embarrassing.”

If the Thompson Center is ultimately torn down, it won’t be the first time a historic building came and went on the site.

The old Sherman House hotel stood on the corner in various forms beginning in 1837, the year Chicago was incorporated as a city. Over the years, its guests included Abraham Lincoln, Al Capone and Ralph Waldo Emerson.

It was first called the City Hotel and saw a number of additions, tear-downs and rebuilds until 1871. That’s the year when hundreds of guests and hotel workers stood on the roof to watch the Great Chicago Fire. Luckily they evacuated before the hotel itself burned to the ground.

A new version went up two years later, with extra floors added over the years. It was popular with mobsters and politicians alike.

Capone and Bugs Moran met at the Hotel Sherman in 1926 for a peace summit mediated by Mayor “Big Bill” Thompson.

The hotel’s College Inn was a popular nightspot for jazz fans during the big band era. Everyone from Fats Waller to Frank Sinatra and the Dorsey Brothers came to entertain the city’s high society.

Mayor Richard J. Daley made it the headquarters of the Cook County Democratic Party.

The hotel ultimately closed in 1973 and was eventually torn down to make way for what was first known as the State of Illinois Center.

When the building opened in 1985, Gov. Jim Thompson called it the first office building of the year 2000, describing it as “open,” “honest” and “friendly.”

But by the time it was named for him in 1993, Thompson acknowledged it wasn’t everyone’s favorite.

“Chicagoans love it or hate it,” Thompson said, “but they talk about it. That’s Chicago style.”