The problem with shaving your chest is that you have to shave it everyday if you want it to stay smooth.
The only way around that is getting it waxed once a month. I think waxing is a waste of money though.
Just shave it once a week or before you know you're going to take your shirt off
Make sure you use a cleanser and lotion as your chest can break out just as easily as your face and get razor bumps after shaving.