Fixing paint chips involves a little sanding, spot priming, some spackling paste or drywall mud, retexture the area if necessary and repainting (touch up) the area affected.
For smooth un-textured areas, lightly sand the area to smooth or "feather" the rough paint edges and prime with a quick drying primer. Kilz or something similar works great. For textured areas, check for any peeling paint and prime the area.
Now apply some spackling paste (for small areas) or drywall mud (for large areas) to the area. Cover the area so it is even with its surroundings. Lightly sand the patch smooth and reprime. Now you can either touch up the area, if you have left over touch up paint, or apply a texture to match the rest of the ceiling.
Unfortunately, there isn't a real easy fix.