Moral dilemma--not sure what to do

Tricky situation there.
I'm assuming she doesn't know that you know you know that she cheated on you, so I would definitely sit down and have a chat with her.
Don't tell that you read one of her conversations, and see if she'll just admit to you the truth without you having to bring that point up. If she isn't honest with you and you still want to be friends with her, then just suck it up and be ultra-careful in the future :s
However, if in your mind, you think that confronting her with proof will lead to her confessing all, then go for it. If it results in the more likely reaction of anger (to cover up the fact that she cheated), then you'll have to gauge if you want to risk it and press the matter, or just clearly state your view on things (possibly an ultimatum but it doesn't have to be so harsh, dpeending on your mood).

Jam it back in, in the dark.