Clean the chipped area with a detergent and water solution. Rinse thoroughly with clear water. Wipe the area with a clean cloth moistened with rubbing alcohol.
Sand the chipped area with fine-grit wet and dry sandpaper, roughing the area slightly so that the epoxy will adhere. Allow the area to dry thoroughly before proceeding.
Mix the epoxy according to the package directions in a small plastic dish. Mix in appliance paint to get the desired color.
Fill the chip with the epoxy mixture using a craft stick or toothpick, depending on the size of the hole. Use multiple coats of the epoxy for deeper chips, letting the product dry between coats. Smooth the epoxy with the edge of a craft stick or toothpick. Remove excess compound with a single-edged razor blade.
Saturate a cotton swab with fingernail polish remover. Wipe excess filler from the sink with the polish remover.
Allow the epoxy to dry for at least 24 hours before using the sink. Wait several days before scrubbing the area to allow the product to set.