An opportunity is when you're given circumstances that make it possible to do something / that make it possible for something to happen: Because Joe quit, I was given the opportunity to get a promotion. (Joe quitting are the circumstances, and now it's possible to get a job)
Chance can mean "the possibility of something happening" and "an opportunity to do something". But it usually means that you won't know the outcome of the chance.
"Take a chance," would mean, "make a gamble." "Give (it/me/them) a chance," means "give something an opportunity/try, even though you don't know what the outcome will be."
