Paint chips: to fill or not to fill?
Paint will not fill the depression or smooth out the transition. I recommend filling the depression with joint compound, no tape needed. It may take a few passes to fill it nicely, but with thin layers it will not take too long before you can apply additional coats of compound. You probably do not need to fill the entire depression, just feather the transition out. Stop when it looks good to you.
Sanding the paint edge lightly first will help you blend the two together. If you find the paint edge is flaking off the wall, scrape upward with a putty knife until you reach an area that is secure. Otherwise it may just separate on you later, undoing your repair job.
Finally, you may want to prime over the joint compound before repainting, especially if you want to try to get the match with the old area good in one coat.