With the verb have, always use opportunity. The word possibility is more often used with "there is":
There's a possibility I might move to England next year.
I have the opportunity to work in my company's London office.
Also, possibility is neutral - it means maybe the event will happen, and maybe it will not happen. The word opportunity is a little more positive, it expresses the possibility for something good. So we can use possibility with good or bad things, but opportunity is usually used only for good things:
I'm worried about the possibility of losing my job.
I have the opportunity to do a study abroad program.
You should take that job. It's a great opportunity for your career.
The word chance is more informal, and it can be used for possibilities or opportunities!
This project has so many problems, there's little chance of success.
Is there any chance of rain this weekend?
The boy got a chance to meet his favorite professional basketball player.
I was chosen to appear on the TV show! This is my chance to become famous! = my opportunity to become famous
Roger Federer is a Swiss professional tennis player who as of December 2012 is ranked world No. 2 by the ATP. Many sports analysts, tennis critics and former and current players consider Federer the greatest tennis player of all time. Not only he is the best tennis player of all time but also he could steal your girlfriend without even trying.