If it's not visibly cracking, flaking or compromised, you may be able to just repair the chipped areas. If the chips are deep, you may need a filler such as our Appliance + Porcelain Repair Kit, but for smaller chips, the following should work well:
Sand off any old paint and try to get the area with the chip as smooth as possible. Make sure to wipe off any dust before applying Soto's Appliance + Porcelain Touch Up and ensure the surface is clean (free of oils and dust) and completely dry (our Shop Cleaner + Degreaser or our Multi-Surface Spray Cleaner works well for this, and is available in five sophisticated scents as well as unscented). Apply light coats and allow it to dry in between. You may need to apply several coats. The longer you allow the paint to dry and cure, the harder and more long-lasting the finish will be. This means try not to use the sink for as long as possible to allow the paint to thoroughly set (it usually takes 1-2 weeks to thoroughly cure and harden, depending on environmental factors such as temperature and humidity).
If the area is the interior of the sink (i.e., it will be exposed to water) and you need to use it before it has thoroughly cured, you may be able to cover the area by taping plastic wrap over the area while the sink is in use, and then uncovering it to let it cure/dry when not in use.