Despite its health-crazy reputation, parts of Los Angeles are plagued by obesity rates that rival any city in America. Now, the city may join a growing roster of local governments aiming to put their residents on diets by cracking down on the fast-food industry.

Jan Perry, a Los Angeles city-council member, is spearheading legislation that would ban new fast-food restaurants like McDonald's and KFC from opening in a 32-square-mile chunk of the city, including her district. The targeted area is already home to some 400 fast-food...