To me, the word "opportunity" would not work in that sentence -- the word "opportunity" seems too definite/specific. The word "opportunity" would suggest that it is possible to be given a definite option to choose a specific result. However, it is unlikely that any one person can offer you the option of "becoming a famous artist". There are too many variables involved in achieving "famous artist" status, and I think that's why I prefer the word "chance".
I hope more people will post their opinions for you. That might help you develop a better feel for the usage of each word. I'd also suggest searching resources such as the BNC, COCA, the New York Times, etc. for examples of usage for each word
in context.