Here is how I do repairs on chipped paint.

First off. Get some wax and grease remover. (3M make a good one that is found at any hardware store.) Wipe the whole plane down before you do any work. Feather out the hard edge of where the paint chipped off with some 220 grit followed by 320 grit. Lightly suff the surrounding are with a scotch brite pad to dull the the surrounding finish where the repair will be done. Wipe down again with wax and grease remover. Apply some primer to the area (2-3 coats leting dry between coats) . Wet sand the primer with 400 grit wet/dry paper to get level. (I like to give a light dusting of black paint over the primed area to use as a guide coat. The black will show all the low spots/imperfections. Once the black is gone, all surface are level. You may half to a second set of primer coats depending how it sands out.) Make sure that the primer edges are feathered out or they will show up as a hard line once the paint is applied.

Once you are ready to paint. Lightly scuff the surrounding paint with a scotch brite pad to give the color coats something to adhere to. Wipe down AGAIN..... with wax and grease remover. Tape off where the purple meets the white. Start with applying the color only to the area where you see primer. Do it in light coats! NOT HEAVY COATS!!!! Let dry between coats of color. Once the primer is covered (so you can not see it anymore through the color) with the color, start feathering (blending) the color over the rest of the area you have taped off.

Do the same for the white as above. Depending what type of paint is on the plane..... there maybe more steps to follow. Once all the painting is done. Buff the paint out.

This gives you an idea of what to expect. It is not hard!!!! Just take your time and things will turn out. The worse thing one can do when painting is hurry through it.