I am a firm believer that being drunk is no excuse. I'm also a firm believer that if you love someone, you're good to them. Period. So first of all, you should think hard about whether you really "LOVE" your boyfriend.
Personally I think that word is typically used too generously. There's nothing beyond love, and if you're cheating on your boyfriend you haven't truly reached a state of "love".
So I think you have 2 options:
1: Tell him the truth: It'll be difficult obviously, but just sit him down and say "I got too drunk and made a mistake. I wish I could take it back, but I'll understand if you don't feel like you can trust me, or want to break things off." If he respects himself he will probably leave you. Of course, he may be willing to try to work through it, but it's NOT going to be easy. Your relationship will never be the same, so be prepared for him to have lots of resentments towards you and have little trust in you.
2: OR you could take a risk and keep it to yourself in order to protect him. The problem is if anyone else knows what happens they might tell your boyfriend for you. It's best to tell him yourself rather than letting him find out. He'll feel more betrayed that way. And if he respects himself, again, he will probably leave you.
Of course, this is just my opinion. But I tried to forgive someone for cheating on me and everything beyond that point was basically a nightmare, so be prepared to work hard if he does feel like giving you another chance.Good luck!