From 1937, It's Love I'm After marks the third and final pairing between Leslie Howard and Bette Davis, who are just wonderful together and really ought to have done more comedies.
He plays Basil Underwood, an egotistical ham actor and she plays Joyce Arden, his equally egotistical, long-suffering girlfriend and co-star. And a very young Olivia de Havilland (who's still alive along with her sister) plays the crazy fan girl heiress. Eric Blore is also terrific as Basil's valet/friend.
The plot is one of those slamming doors and swapping partners Thirties screwballs that are such a joy to watch.
"I was in love with Clark Gable last year"
"Who's Clark Gable?"
It's Love I'm After is available on Region 1 as part of the Warner Archive overpriced DVD Collection and is occasionally shown on TCM. There is a torrent of it, but don't download it because it cuts off the last five minutes.
Here is the best quality clip that I could find: