CHANCE: how much probability there is that something will happen, or a gamble or risk, or a good time for an event, or an unseen force (the universe?) that makes things happen.
-- There is no chance he will recover. (The probability that he will recover is zero.)
-- You're taking a chance by drinking that old milk. (You're taking a risk because the milk might be spoiled.)
-- I didn't have a chance to tell her I loved her before train departed. (There wasn't a good time to tell her my feelings because we were running for the train.)
-- We had a chance encounter. (There were some cosmic forces that made us cross paths and we could not have planned for this.)
OPPORTUNITY: favorable conditions, or a chance in which you are more likely to win than to lose.
-- When opportunity knocks, open the door. (When something favorable comes by, do something to help it along)
-- Thank you for the opportunity to interview for this position. (Thank you for giving me the possibility of getting this job, which would be a favorable thing.)
-- The price of the house has gone down, so it's a great opportunity to buy. (The price will likely go back up, so it's favorable to buy now.)
If you say "go to the party, there's a chance you'll meet someone new" it means there might be someone new, or there might not, it's a gamble, but try anyway.
If you say "go to the party, there's an opportunity to meet someone new" it means that this party has some eligible people and it is favorable to you if you go.