The way I see it, "chance" has to do more with unexpectedness in quite a number of cases. Consider the following sentence:
Leave nothing to chance.
That is "study whatever you are up to carefully and watch out".
On the other hand, "opportunity" implies more than just chance:
For more than two centuries, America has been a beacon of hope and opportunity for people from around the world.
I found this nifty explanation by an Englishman online:"A chance is available in a situation where you are surprised or you had not expected it to happen. In a sentence like: As we were in the city at the time we had a chance to visit the museum.
Here this is something that we had not planned. In this sentence: If children work hard at school, they have an opportunity to go on to higher education. Here this is something that is planned and can also lead on to something else."