I'll give you a chance.

Why do you ask?

It’s no different than “ I”ll
give you a cookie.”

Is the concept of “giving a person a chance” your real question?

Yes, because I once wrote "a chance", and my friend said it should be "second chance", which causes me to be confused.

You should have given more context at the beginning. Your friend may well be right.

A second chance is a long established term used when someone has initially failed at something.

That doesn’t make,’I’ll give you a chance,’ wrong or grammatically incorrect.

And it shouldn't necessarily be second chance unless there is some context you aren't providing. It could be the first chance.

Exactly, which is why I said their friend may be right, not that they were right.