Wrong, written for the 1934 (horribly sexist) musical "Dames". Initially performed by a very young Dick Powell (in an excellent tenor), sung to Ruby Keeler (who looks like my cousin Peg). Here's one Youtube link. Here's another, with a little bit of the incredibly psychedelic Busby Berkely choreography.
After you know, you can clearly hear the 30's origin. The 1st one of these I had was "Let's Fall In Love", which I would have put at 50's until I got a 1934 recording of Annette Hanshaw doing it.