Is there a way to fix a small chip in a wall's paint?
If this is no deeper than about 1/16th of an inch you can fix this with a can of wall texture. Any deeper and you'll probably want to get some spackling paste. 

If you get the paste, smear it in, and scrape it level with the wall using a plastic scraper. Let it dry. Dap Drydex is good for this because it starts out pink and turns white when its dry.

Next, spray on the wall texture. A knockdown knife will make it easier to get the texture to match your existing texture.You might need to redo this step a couple of times to get it right if you're new at this. Get a wall sanding sponge and take the dried texture off if you redo it. You also might want to use the sponge between the spackling step and the texture step and maybe even before doing the spackling. If you get the basic tools you need (scraper, wall sanding sponge and knockdown knife) as well as the materials(spackling and wall texture) you can rinse and repeat until you get it looking perfect. It takes a bit of practice to get it looking right.

Then, apply paint and you're done.