LOS ANGELES (CBS) — Could it be the end of spicy chicken chunks and cheeseburgers for students in the Los Angeles Unified School District?

READ MORE: Black Friday: Another High-End Store Is Robbed, In String Of Six LA Smash-and-Grabs

Superintendent John Deasy and reality show chef Jamie Oliver announced big changes for LAUSD school lunch menus on ABC’s Jimmy Kimmel Live! Tuesday night.

The district, which is the second largest in the United States, will no longer offer chocolate- and strawberry-flavored milk, which both contain more sugar than soda.

READ MORE: Possible Lakewood Home Depot Robbery Suspects Arrested in Beverly Hills

Oliver has not been allowed to bring his cameras inside LAUSD cafeterias, but he has criticized the district’s menu on his reality show, Food Revolution.

Deasy, who says the menu will be changing for the 2011-2012 school year, tells KNX 1070 he doesn’t expect much resistance on the district’s policy change.

MORE NEWS: Fox, Hield Lead Kings Over Lakers 141-137 In Triple OT

“I think the board has done a number of steps in terms of removing soda and junk food, and reducing sodium, and completely revamping the menu,” Deasy said. “This is definitely the logical next step.”