It has happened to me before, usually when I am first starting and need to lose some weight. It doesn't happen anymore, bra or no bra. I do wear tech shirts I got from races though.
The way to take care of the problem right now is bandaids. Think of them as a mini-bra, LOL.
There is also a product called body glide that rolls on like a deodorant stick to reduce chafing.
Conform and be dull. —James Frank Dobie, The Voice of the Coyote