The "me first" attitude

I guess my little Chloe has not learned what it means to share or to let others go first. She likes to win at everything and wants to do things first before her sister or even before her parents. Just now she is playing candy land with Ellie and Ellie won. Chloe got upset and started throwing the little people. How do you teach your children to let others go first or the right way to lose. We have tried to tell her its not about winning or losing but about having fun. To her that is hogwash! When Ellie tries to play by herself, Chloe gets upset cause Ellie won't play with her, but if Ellie tries to play with Chloe then we have a tantrum on our hands.. We just can't win. I think I'll go throw a tantrum now too!!