CHICAGO — The Nets don’t have the face of their franchise.

Lottery luck Sunday in Chicago (3 p.m. on ESPN) could change that.

Brooklyn hasn’t drafted a homegrown All-Star in over a decade, dating back to Brook Lopez. But in a generational class with a trio of projected franchise-changers, the Nets go into Sunday’s lottery tied for the best odds of winning the No. 1 pick (14.0 percent) and of landing a coveted top 3 pick (40.15 percent).

BYU wing AJ Dybantsa, Kansas guard Darryn Peterson and Duke big Cam Boozer are all viewed as face-of-the-franchise stars, with North Carolina’s Caleb Wilson an elite prospect who could conceivably turn that Big Three into a Fantastic Four.

“If I got another guy here who really is able to create and draw some attention, and now I’m getting two or three wide-open 3s a game, it would really help us,” Michael Porter Jr. said on the Road Trippin’ podcast.

“That’s what we’re [looking for]. I’ve talked to the front office, and that would be a big thing for us. I think we’re going to get a good draft pick, and then we’ve got the most money in the NBA to go get a really good playmaking two-guard or point guard; that would just help.”

Despite a glaring need for a playmaker, Brooklyn is talent-poor enough that it will almost certainly draft the best available player and trade or sign a guard if needed. With the Nets owning Houston swap rights on next year’s pick — in a class already seen as weak — Sunday marks their best shot at a young star.

Dybantsa, Peterson or Boozer are all perceived cornerstones, and Wilson could be as well. If they fall outside the top 4, there are a host of guards in Kingston Flemings, Darius Acuff Jr., Keaton Wagler and Mikel Brown Jr.

Could sliding as they did last year prompt Brooklyn to be more aggressive in the trade market?

They can’t dip below the seventh pick, but their likeliest landing spots are sixth (26.02 percent chance) or fifth (14.82 percent chance).

A franchise that has been one of the league’s most star-crossed will send owner Joe Tsai to the team drawing room and Hall of Famer Vince Carter to the dais seeking some much-needed luck.

“I’m excited to be representing the Nets at the draft lottery this weekend,” Carter said in a message recorded for Brooklyn fans. “I’m hoping I can bring us some luck. Stay tuned. Go Nets.”

The Nets need luck more than their lottery co-leaders, as Indiana reached the Finals a year ago and Washington added Anthony Davis and Trae Young. Brooklyn lacks a star, and this is its best opportunity for one.

To drive that point home, the Mavs, Spurs, 76ers and Hornets got the first four picks last year, and vaulted from averaging 29 wins to 44. But the Jazz, Wizards, Pelicans and Nets settled for the next four selections, and after averaging 20.5 wins were right back in the cellar again with 21.

The lottery has rarely been kind to the Nets, with top 8 odds 10 times and only moving up twice: winning in 1990 to land Derrick Coleman and again a decade later to pick Kenyon Martin. Within two years they’d made the Finals.

Their lucky charm in the drawing room that day in 2000 — ex-team president Finn Wentworth — told The Post a successful Sunday could spark a similar meteoric rise.

“Ours was the worst draft. This is arguably the best draft in the modern era,” Wentworth told The Post. “They don’t need to get the first pick in this draft, it’s so deep. If they get one of the top 3 picks, they’ve got a force to coalesce around.

“If they can get one of the top 3 picks in this draft, they can coalesce around this guy, that’s going to go ahead and become a cornerstone.

“This is one of those drafts where it’s very, very deep. You have three or four guys that are A-pluses, and then you have a bunch of A’s.”