During which war did the graffito 'Kilroy Was Here' originate?

During which war did the graffito “Kilroy Was Here” originate? It originated, in its familiar wartime form, during World War II.

The phrase became popular among American servicemen in the 1940s, who wrote it on walls, vehicles, equipment, and places they visited. The accompanying cartoon—usually a bald figure with a large nose peering over a wall—was connected with the British “Mr Chad” doodle, and the two traditions eventually merged.

The exact origin is not completely settled. One widely repeated theory points to James J. Kilroy, a shipyard inspector in Quincy, Massachusetts, who supposedly used the phrase to mark rivets he had checked. Other wartime accounts credit an airman named Francis J. Kilroy, while earlier examples have been claimed but are unverified. Thus, World War I is not the standard answer: the expression’s worldwide military popularity belongs to World War II.