LONDON — In Britain, KFC has added a twist to the perennial riddle, “Why did the chicken cross the road?”

“The chicken crossed the road,” the fast-food chain said on its website. “Just not to our restaurants.”

The company found itself on Tuesday in the throes of a widespread chicken shortage for a third day running, after a hiccup in its supply chain forced half of its 900 outlets in Britain to close.

In one of the KFC holdouts, in Central London, a “limited menu” was on display, and one employee warned at noon that popcorn nuggets and corn were running out fast.