“Every great city has a river,” said Steve Reizes, 50, a property manager who occasionally bikes along part of the river to commute between his home in Sherman Oaks and his office downtown. “They market riverfront properties and restaurants and all kinds of things. Why shouldn’t we have that, too?”

The 280 spots for the trips sold out within 10 minutes this month. Mr. Reizes used two computers to ensure that he could get a pair of the $50 tickets, a strategy usually associated with diehard fans looking for seats at a hot concert.

Just a few years ago, the Army Corps of Engineers decreed that the river was not even a river, with parts of it too dry to be considered much of a waterway. But last year, the Environmental Protection Agency reversed that decision and said that the 51-mile river could be navigated like any other, although parts of it can dry to a trickle at times. This summer, the corps granted a limited permit to the Los Angeles Conservation Corps that would allow a set number of paddlers on a 1.5 mile stretch for seven weekends.

So with the sun already blazing one recent Sunday morning, George Wolfe, the founder of L.A. River Expeditions and the leader of the trips, gathered the group for a brief safety lesson. Mr. Wolfe, who traveled the length of the river on an unauthorized three-day trip several years ago, gave his standard warning: You never travel the same river twice. Just last week, he spotted an oil barrel in the water.

“If you fall in the water, don’t panic,” Mr. Wolfe said, as a few in the group laughed nervously. For many of them, it would be their first time in a kayak. “The first thing you should do is stand up. Chances are it’s just a few inches.”