Well, the Navy's been there fairly recently, the single engined A-4 Skyhawk, the F-8 Crusader, and the A-7 Corsair which was based on the latter all saw heavy service in Vietnam. And per Wikipedia, the latter replaced the A-1 Skyraider (to the extent a jet like that could) and the F-100.

But for the obvious reasons they vastly prefer two engined planes, plus I've read the F-35's single engine is so big their current logistics system will have trouble getting new ones to a fleet at see, I assume this means it can't fit in a C-2 or maybe V-22.