How do I choose a Maid of Honor when my two best friends hate eachother?

My two best friends are oil and water. It's so bad, that when I plan get-togethers, I alternate which of the friends to invite so that they don't have to see one another. I'm on the verge of being engaged, and I don't know how to go about this. I'm leaning toward...let's call her Fran. If I pick Fran instead of...Nicole, Nicole will be upset and vice versa. Help!