With the verb have, always use opportunity. The word possibility is more often used with “there is”:
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:
The word chance is more informal, and it can be used for possibilities or opportunities!