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
After more than 10 years as an advertising and commercial photographer Sephi Bergerson closed his studio in 2002 and moved to India with his wife and 10 month old baby girl to follow his dream to be a documentary photographer. Sephi s work has been featured in books and publications worldwide and has won international acclaim. His most inspiring photo projects address cultural and humanitarian issues from polio and HIV to rural development and education.