Infidelity

Is it possible to truly forgive someone for cheating?

About a week ago I found out that my boyfriend cheated on me. I confronted him about the situation and he told me what happened. One night he got really drunk hanging out with some friends and those friends invited other people over and he ended up sleeping with one of the girls. He did not remember it happening at first, and I believe that because I talked to him that night and he sounded very lost. But the fact that he did eventually remember it happening and only admitted to it when I confronted him really bothers me. He genuinely seems sorry and ashamed by what he did but is that enough? Is being "black out drunk" something that makes it acceptable.

I don't believe it does but for some reason something in me wants to give him one chance. I don't really know what to do. We talked about it for 2-3 days but now it feels like we've pushed it under the rug.