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Buy a 2-component epoxy kit for chip repair. Scrub the damaged area with a sponge and soap or tub cleaner, then dry it. Follow the directions on your epoxy kit to mix the 2 components together. Apply the epoxy to the chip with a small spatula, paint brush, or bottom of a matchstick. Let the epoxy dry, then sand down the surface with 400-600 grit sandpaper.

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Look in the adhesive or bathroom repair section of a home hardware store. Buy a kit that comes with both the catalyst and hardener that you will mix together to create the epoxy.  Most epoxy chip repair kits come in shades of white to match the most common color of bathtubs. Try to choose a kit that will closely match the shade of your bathtub, or 2 kits that you can mix together to create the right color. Epoxy repair kits work to fix chips in all kinds of bathtubs including ceramic, porcelain, acrylic, fiberglass, and enamel tubs. Use warm water and dish detergent or a household tile and tub cleaner to clean the chipped area. Thoroughly dry the area with a clean rage after you finish cleaning it. You can also use acetone or rubbing alcohol to clean the area. Any product that removes grease and soap scum will work to clean the chip. Some epoxy kits come with a mixing tray and stirring stick for you to use. Mix the epoxy in a disposable tray with a toothpick or matchstick if your kit didn't come with the mixing supplies. It's a good idea to set the tray on a piece of cardboard or some scraps of paper to catch any spills. Scoop up a small amount of the epoxy with your chosen utensil. Spread it carefully in a thin layer over the chip by working in 1 direction and smooth out any spots where it pools.  Make sure that anything you use to apply the epoxy is disposable. It will be hard to get the epoxy off of anything it touches. It's easiest to start with a small amount of epoxy and add more layers than it is to put too much on and remove it. Follow the directions on your epoxy kit to let it fully dry. Gently sand the surface with 400- or 600-grit sandpaper until it feels smooth like the rest of the tub.  Some epoxy will set in 2-3 hours, at which point you can sand. Other kits may advise you to wait up to 24 hours before sanding. You can add another layer of epoxy after sanding if you can still feel the chip. Then repeat the process.