Corian, a nonporous solid surface material, is made to be durable and easily repairable by its manufacturer, DuPont. It is often used for kitchen and bathroom counters. If the chip in the Corian is shallow enough to sand out, try that first. You may wish to use the sandpaper recommended by DuPont. Filling in a small chip with super glue is another do-it-yourself option. For a larger and more noticeable chip, you may have to have it professionally refinished.
Clean the Corian surface thoroughly where the chip is located, using a non-abrasive cleanser and a sponge. Rinse the surface and let it dry.
Wet the surface of the Corian. Rub the Corian with a fine-grained abrasive sandpaper pad. Increase the roughness if needed to remove the chip. Switch back to progressively finer grains to smooth the surface again. Clean the pads if they become difficult to use. Skip this step if the chip is deep but not very wide.
Apply super glue to the chip so that it comes right up to the surface if the chip is deep but not wide. Wait for it to fully dry. Sand the surface until it is at the same level as the rest of the Corian.