There's a stretch of the Los Angeles River in the Elysian Valley, roughly midway along its 51-mile route to the sea, where native willows rise from the east bank and arundo—an invasive grass—closes in from the west. If you're lucky enough to be out there in a kayak, and there's no train rushing past on the tracks above, you will hear something very strange in this city of millions: quiet.

On a recent evening, Omar Brownson, the head of the L.A. River Revitalization Corporation, leaned back in his red plastic kayak, closed his eyes, and listened to the soothing sounds of birds singing and water slipping over rocks.

Wait—Los Angeles has a river?

Well, sort of. Once upon a time, gathering waters from an underground aquifer in the San Fernando Valley and from the surrounding mountains, the river nourished a lush coastal plain, creating rich soils that covered the region. Today, it's largely encased in concrete and barely recognizable as a river.

But thanks to an agreement this spring between the city and the federal government, the overlooked waterway is slated for a $1 billion restoration effort. That plan covers an 11-mile (17.7-kilometer) section of the river that runs roughly from Glendale to downtown. The ultimate goal: transform a neglected wasteland into an urban oasis—a 51-mile greenway, complete with bike path, bridges, parks, public art, waterfront businesses, and, at the center, a thriving river. Imagine New York City's High Line, but aquatic and at three dozen times the scale.

"The L.A. River," says Brownson, who grew up in Los Angeles, "is one of the few chances we have to hit the reset button."

View Images Participants in Paddle the L.A. River, a program run by the L.A. Conservation Corps, kayak through the Sepulveda Basin Recreation Area in June 2014. Photograph by Bill ALkofer/The Orange County Register/ZUMA Press, Inc /Alamy

Taming the Torrent

When the Tongva Indians first came to the area, as early as 5000 B.C., they settled on the river's lush banks. Cottonwoods and willows towered above the water, and bears foraged in thick tangles of berry bushes.

Much later, as Los Angeles boomed in the mid-1800s, European settlers built in the river's floodplain. For much of the year, it was a meandering creek. But winter rains turned it into a cascade, overflowing its banks and washing away whatever was in its path. That path shifted dramatically: At some periods the river emptied into San Pedro Bay near Long Beach (as it does today), at others into Santa Monica Bay to the northwest.

Over the next century, a series of catastrophic floods leveled buildings and swept away residents. In 1934, after a devastating flood on New Year's Day, Congress stepped in, authorizing the Army Corps of Engineers to tame the river. They deepened its channel and encased three-quarters of the river in a concrete ditch, fixing it once and for all in its current—artificial—path.

Since then, it has looked more like an irrigation canal or a "water freeway," a narrow ribbon of water running at the base of gray concrete slabs. John Travolta's iconic car race in the movie Grease? It took place on the bed of the L.A. River, just south of City Hall.

In 1985, environmentalists began campaigning to restore parts of the river to its natural state—a vision that took shape over the intervening decades, with help from a few key champions of the river. Today, that vision is officially under way. Mayor Eric Garcetti, who took office a year ago, has made the river a focal point of his administration—even traveling to Washington to lobby President Obama in person.

In late May, the Army Corps of Engineers approved the far more ambitious of two competing proposals to revitalize the river. The plan, known as Alternative 20, involves tearing down roughly six miles (9.6 kilometers) of concrete walls and replacing them with a series of green terraces and wetlands, many of which will merge into parks. It will be several years before the concrete removal begins; the Army Corps plan still needs congressional authorization.

Beginnings of a Greenway

In the meantime, though, the city has been buying up chunks of land—most of them barren lots of crumbling asphalt—on the river's eastern flanks, in a bid to build a chain of parks where, says Brownson, "it'll be seamless in terms of how the city and the river come together."

Brownson's organization is raising money on a project-by-project basis, bringing together funds from city, state, and county coffers as well as from private and philanthropic sources. Their first major construction project is a $9 million pedestrian and bicycle bridge that will connect the east side of the river to a bike path and the 4,200-acre Griffith Park on the west side. Visible from the I-5 freeway, it's intended as a symbol of the river rising again.

Metaphorically rising, at least. Whatever happens, the Los Angeles River still has to function as a flood control channel. "Anything we do cannot lessen that," says Brownson. The river can't be allowed to shift its course over a large floodplain, as it once did, because there's now a major city in the way.

Brownson sees that constraint as similar to the one imposed on a poet by the sonnet form. "How can you be creative," he says, "within a set number of syllables and stanzas? Instead of it being a limiter of what's possible, it's just a structure for how do you create within that frame." The finished project, he says, will have to blend together wetlands and picnic spots, flood control terraces and bird habitat.

"This has the opportunity to become a regional natural resource," says Barbara Romero, the city's public works commissioner. "It's basically redefining people's opportunity to experience nature in their neighborhoods."

Much of the river is still inaccessible even to locals. In one neighborhood, 27 streets dead-end at the river but only four have proper access; the rest end at chain-link fences. One of the revitalization corporation's projects, called Street Ends, will help communities design and build their own gateways to the river.

View Images A man fishes along the Los Angeles River in June 2014. A plan to return the river to a more natural state will cost an estimated $1 billion. Photograph by Patrick T. Fallon, Bloomberg via Getty Images

Kayaking Through Elysium

Last summer, four kayaking companies set up shop, offering tours of two distinct stretches: a float through a calm, flat section called Sepulveda Basin, or a wilder journey down the Elysian Valley that involves four small rapids and considerable navigation among rocks. In both sections, the river—due to engineering challenges that the Army Corps faced during the channelization—retains some of its soft bottom rather than running over a concrete base.

When I kayaked the Elysian Valley with Brownson, as part of a group led by two local artists who run L.A. River Kayak Safari, the wildlife on display included a heron, an egret, several cormorants, and a smattering of ducks. Still, for much of the two-mile journey downriver, it was hard to forget that we were in the center of a major city. Trucks rumbled on freeways; double-decker commuter trains thundered past. And those concrete walls remained in place.

The L.A. River will never be wild. Even the water running through it is domesticated: 80 percent of the flow now comes from a wastewater treatment plant in the San Fernando Valley, next to Sepulveda Basin. Steven Appleton, who runs the kayak company and has visited the plant, advises his clients not to drink the water but not to worry about accidental ingestion.

The river project is primarily a sweeping exercise in urban renewal rather than nature restoration. Ed Reyes, a former city council member who was instrumental in pushing the river agenda, says he saw an opportunity to make smart decisions at a crucial time—expanding bike paths, reinstalling wetlands, turning abandoned industrial areas into parks.

"If we don't begin to identify spaces along the freeway, along our corridors, think about how we get water to our trees—if we don't build in these policies as new developments come online, we're going to miss an important phase in our city's growth," Reyes recalls thinking. The river, he believed, could be the catalyst for a whole new framework of city planning. "We have to formalize it through the river corridor," Reyes says, "and branch out from there, like a nervous system."