My boyfriend of 3 years cheated on me, should I give him another chance ?

That highly depends on how you feel about this situation. Are you willing to forgive him? Is he worth it? There is no excuse for cheating, but it doesn't mean that the person isn't sorry for what they've done. It'd be best to think this through, analyze the pros and cons, but no matter what - put yourself and your happiness before anyone, including him.

If he truly does feel severely sorry and guilty, has no emotional connection to the person that he cheated with, and is willing to move on and build a stronger relationship with you, he deserves a chance to show you that he's not a bad person. But it's up to you to give that chance.

Well, if this is the first time he has cheated then yeah sure. Why not ? But if this has happened more than once. Then he doesn’t deserve anymore chances. A snake always remains a snake no matter how many times it sheds its skin and so he is gonna remain the same liar and cheater no matter how many chances you give him and he squanders them all. You deserve so much better than someone who cheats. So if not for anyone else then for your own dignity and respect do not give a cheater more than a second chance.

I think when anyone asked this question, it is because they know the answer. If you felt as though they have changed and the relationship that could form would be positive for both, then you would not ask the question. Take a step back and look at the relationship from before as though it was a friend that had gone through it. What would you tell them about the question? Do you think that the trust could be built back, or would it stick with you? An important part of any relationship is trust and it is something that is built over time