My girlfriend cheated on me, should i give her a second chance?

My girlfriend and I have been dating for over a year. Last December she moved away to another state. We have made several plans for college, careers, etc. We've been away for over 4 months now but i plan to fly there this summer. Long distance relationships are tough and i have been really depressed since she left and no longer even hang out with my best friends. As of last month she has been much happier from becoming friends with an old friend again and hanging out with her often. Last monday she talked about how she was really excited for friday. I asked why and she said shes hanging out with her friend. She was acting sort of strange and i usually don't ask nosey questions but i decided to ask what their doing friday and she said going to a friends house. The rest of the week went really well being reminded of how soon summer and being reunited is and alot more phone calls and skyping than normal. On friday when i asked whats up she replied at that friends house. She then texted a few more times before she went a couple hours without texting me. I hate to think anything could be happening as she tells me how important it is for us not to drink or anything that could threaten our relationship from this far. She texts me in the morning about how she cant stop throwing up. This raises my worries more but i ignore it and try to help her feel better. We joked around and talked through the day until she started talking about riding a motorcycle with someone on monday if its nice out. I couldn't hide my uncomfortableness about last night any longer and unintentionally my texts started sounding unhappy. She asked if she did anything and then talks about how her friends say she should leave me. I answer in one word replies because i dont know what else to say. She says she thinks she should tell me something and i quickly ume and ask if she cheated on me or something. I thought that was kind of offensive thing to ask but she told me the truth of everything that happened. She went to a party with the 3 friends shes been hanging out with lately. She got drunk and made out with a guy and then the cops came and sent them all home. I hope she only made out with him but would she have gone further if the cops didn't show? Also was she planning to go riding on a motorcycle with him next monday? She sincerely apologizes what happened and says she doesn't want to break up and wishes it never happened. I still love her so much and its so close till we can see each other, i hate that this happened. I think were broken up now but should i give her another chance? I know the once a cheater always one thing but really do you think it could work? I believe that she feels pretty bad about it.