How to apply the primer over paint on a small chipped area
So it sort of depends on how bad the chipping is.  (posting a picture will allow for a bit more detail in answers)

In general for chipped paint I would recommend the following process. (and yes getting the prime on existing paint is no big deal)


Clean and sand the edges.  Basically, make sure that nothing else is loose.  Take a scraper and chip off any paint that does not adhere to the wall behind it.
Fill the holes with non-shrink spackle.  Use a scraper, apply it, let it dry then sand it smooth with the surrounding wall.
Prime.  You can get away with a spray primer (I generally use the spray Kilz to seal the parts that were patched.
Paint.  So you can brush it on and just apply a spot fix...but the texture of the paint will be different from the walls around it...ideally you should paint the whole wall, but that said you can roll a section of it, and feather out from the main area that needs paint.