What kind of dress should I wear under a backless dress for prom?

The dress is very pretty and flowy, but there is no support for the front of the dress. I'm very small chested and I don't want to go bra-less. I have considered an adhesive bra, but I heard that it will probably come off during the dance if I get sweaty, etc. Are there any other good options? Does the hollywood tape work? Thanks so much!