Should I leave him for cheating?

Me and my boyfriend have been together about 8 months. Today he revealed to me that when we first started dating, he cheated on me with a random girl who's name he doesn't even remember. I'm not as mad about the cheating as I am about the lying for so long. During the time he cheated, we hadn't had sex yet. Actually the same month it happened, that's the month we finally had sex. I don't blame myself for his lack of self control. But I do kind of understand why he felt the need to seek out something I wasn't giving him. Nevertheless, I would have respected him more for just ending things or just talking to me honestly. I told him to give me a day to decide if I still want to be with him. I would like to work things out but I don't want to look stupid or for him to think he can get away with anything and everything. So should I give him a chance to prove himself or leave him?
Should I leave him for cheating?
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