How can you hide tile chips without replacing the tile?

You could try coloring in the brown with a matching tile color. I have done this with other things like plaster on a mirror frame with markers. Or use a craft paint to lighten the brown to the tile. You could fill these spots with spackle and color the spackle. Any hardware store will have that.

How to Repair Holes or Cracks in Ceramic Tile

Patching unwanted holes in glazed tile like this can be a tricky proposition. Here's a solution that may not always be perfect, but will make a big improvement. Polyester resin or auto body filler, often used to repair car bodies. Mix up a small batch by adding some hardener and stirring it thoroughly. Using a putty knife, press the resin into the hole slightly overfilling it. Then just as the material begins to harden while it's somewhat rubbery, trim off the excess with a razor blade.

Next use 600 grit sandpaper to sand the filler smooth. Wetting the paper with water makes it work best. Now it's time to try and match the color of the tile. A porcelain touch up kit which is available at most home improvement centers comes with several different colors of paint. You can also use artists acrylic paints available from Michaels, Hobby Lobby, art supply stores, and online.

The trick here is to mix these different colors together until we come up with one that matches the tile. Apply the paint with a small brush. You can test it on a nearby tile. When you get it the way you want it, then just paint over the patch and let that dry. Give it one final sanding with that very fine sandpaper and you'll have, well, maybe not a perfect match, but something that's a heck of a lot better than what you started with.

My mom used nail polish once one a chipped tile to match the color and the shine the tiles had. Worked real good and lasted a while before she had to reapply it.

I've used matching crayon for tiny spots in the past and it worked well.

I go to the dollar store and buy a bottle (or two, if necessary) of craft paint as close as possible to the grout color. Re “two bottles”, I sometimes have to buy two because I may have to mix colors to come up with a match. I then paint the small chip and it visually helps hide the defect. The paint has stood up extremely well for years through weekly washings, etc. and constant foot traffic.