What am I doing wrong with my crochet project?

I am trying to teach myself to crochet and have started my first project- a scarf. It is a very simple scarf that only uses two kinds of stitches- chain and crochet one. The problem is that my scarf is coming out curly- it curls up on the edges. It's actually kind of pretty, but it's not right. Does anyone know what I'm doing wrong? Thank you.