They are all synonyms with subtle nuances. Chance implies that you leave everything up to luck. If I have a chance of winning the lottery, I can't do anything to increase that chance, and that chance will always be there. Opportunity implies chance, but it follows that hard work can affect. An example would be an interview, you have an opportunity to present yourself well and get a job, and it is more than a chance, because you have a say in it. But an opportunity comes by chance, and it is up to us whether or not we take it. Occasion is what breaks away from this. Occasion is used more theoretically in the case you're probably talking about. An example would be "Occasionally, I go to the beach" or "On the occasion that it rains, I bring an umbrella". It is usually dealing with the theoretical and doesn't target.