This is called "proliferation." Some roses do it most of the time. Some never do it. Some do it when they are over-fed. It was one of the things I detested about the Austin rose, 'Fisherman's Friend.' It may not do it everywhere, but in our garden, it did it in 90% of its blooms.

Here is an article that discusses it:
http://www.romanticgardening.com/2011/06/what-is-rose-proliferation.html

I've never ever seen anything like that...Learn something new everyday..lol

It's also called a vegetative center and besides too much nitrogen I think I've read it can also be caused by some weather conditions during the time the bud is forming. I had one on Quietness once that grew another flower bud right out of the center of the rose. It was weird!

Thanks Guys!