CHICAGO — New Orleans has bucked the odds and won the NBA draft lottery, and now will have the first chance at choosing Zion Williamson next month.

The Pelicans won the lottery for the first time since 2012, when they selected Anthony Davis. And the lottery win comes after a season when Davis wanted a trade — something that might not seem so appealing to him now, not with Williamson likely coming to New Orleans.

Memphis will choose second, New York third and the Los Angeles Lakers will pick fourth.

Williamson says he has never been to New Orleans. That might soon change.

“It’s just another positive event for us,” new Pelicans general manager David Griffin said.

The Pelicans were the biggest winners — and the Grizzlies and the Lakers had reason to celebrate as well. They all moved up, much to the chagrin of teams like New York, Cleveland and Phoenix. The Suns, Cavs and Knicks all had the best chance of winning the lottery, and neither even got as much as a No. 2 pick.

Williamson will have an excellent chance at seeing his name added to the list of other No. 1 picks who entered the league with much fanfare in the lottery era, players like LeBron James, Tim Duncan, Shaquille O’Neal, David Robinson and Allen Iverson.

Cleveland will pick fifth, Phoenix sixth, Chicago seventh, Atlanta eighth, Washington ninth, Atlanta again at 10th, Minnesota 11th, Charlotte 12th, Miami 13th and Boston 14th. That pick was conveyed to the Celtics by Sacramento as part of an earlier trade.

UCF center Tacko Fall, the 7-foot-6 draft hopeful, played against Williamson in the second round of the NCAA tournament. Fall was asked Tuesday who he would take with the No. 1 pick in this draft, and he did not hesitate.

“Zion,” Fall said. “He’s a once-in-a-generation player. He’s different.”