When you "have a chance of winning" something, it means that you might win it. In a contest, if you think that you are better or as good as the other contestants, you can say that you "have a chance".
This phrase is similar to "have a shot at (doing something)" One difference is that you mostly use "have a shot" in positive situations, but you can use "have a chance" in both positive and negative circumstances. For example:
These guys are pros. I don't have a chance against them.