Mate I know exactly how you feel. It took me months before I finally had the courage to talk to my mother. My advice would be to just plan precisely how you'll start the conversation, then just tell yourself "stop being a coward- if I want to rid myself of this, I need to do something" and just open your mouth. Just think that everyday you waste, too afraid to speak, is one day that instead you could be happy and free. I believe for me the conversation went something along the lines of "I need you to promise me that if I tell you something, you will not laugh, or tell anybody else. I'm certain that I have a condition called gynecomastia, i.e. the growth of breast tissue in males. From what I have read, the only treatment is surgery." Another thing to consider that might make it easier to talk to your parents is the thought that your body, with it's "problem" is simply a product of theirs. If you're genes or whatever are messed up, it's because theirs are- it's not as if it's your fault, or something you should be ashamed of.
That said, I'm hardly one to talk- despite talking to my parents about it about 18 months ago and going to see a doctor a couple of times I'm still in exactly in the same position as I was back then. Still with gynecomastia, and still unhappy. At first the GP I went to see tried to assure me that there was nothing wrong with my chest (to be fair, the room was cold so my nipples were small and hard so I guess it looked fairly "normal"), but then conceded that the problem will go away on it's own after my hormones have settled down. I was 17 at the time and have had this problem since age 12 or so- I really couldn't see it disappearing any time soon. I guess that after that I kind of felt humiliated, and haven't really pursued it with my parents since. I think each day the idea of surgery grows more and more attractive to me. My main concern is over the length of the "recovery period"- playing in a band that practices and gigs regularly would make it difficult to just disappear for a month or however long. However I have considered telling my friends that I'm going travelling.
Anyway I hope you find the courage to talk soon. And don't make the same mistake as me- if you want surgery pursue it until the day it is done. I would do anything to replay that last year of my life, having pressed for surgery, and now being content with my body.