My ex-girlfriend wants to get back together, should I give her a chance?

I separated with my girlfriend 10 years ago. We had a son during our two years relationship. She went and got married, had twins, while I did not get any other girlfriend again. Recently, she invited me to a function at their home and announced that she still wants to rekindle our relationship. She says she separated with the father of twins and wants us to get married. Part of me loves her , but I feel it is not right for me because she is the one who initiated the break up. I had caught her cheating many times and she said she wanted to leave me. Now she says she has grown  and changed. Should I give her another chance?