When do you ask for a second chance?

Yes, you should ask for a second chance. Go on a date and talk about how you feel and just to see how things go from there.

If you'd agreed to be friends, don't ask. Not unless he expresses interest in a romantic relationship. If you've AGREED on this and it's not just something the other person said, then you really have no right to ask for another chance to date. But, if they said they'd rather be friends, I would respect those wishes for a while and then after a decent amount of time, ask if they thought it could ever be.