Is it okay to start talking to the girl I like through facebook?

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I am asking this question because I have a hard time talking the the girl I like. I think there is a chance she might like me back. We've talked before so it's not like she has no idea who I am. I was thinking of facebook chatting a few times. Would it be awkward if we only talked a few times this year in person? Also if your a girl, would you like it if a guy facebook chatted you?