SANTA BARBARA, Calif.—Business has boomed for Chick-fil-A franchisee Travis Collins during the pandemic, thanks to surging appetite for chicken sandwiches from his drive-through window.

Now he’s throwing the works at controlling the lines of cars spilling onto surrounding streets. The city council in this affluent coastal city has proposed declaring his drive-through a public nuisance.

Neighbors and city officials say customers hungry enough to brave the crowded lot for Chick-n-Strips or the signature sandwich of chicken with pickles on a buttered bun have caused so many traffic jams, bus delays and hazards on the city’s main drag that something must be done.