I have repaired chips in three sinks and one bathtub. Super easy, but it takes a few days for proper dry time.
I purchased porcelain paint @ HD (not a "kit", just one tiny bottle). Shake very, very well. Turn the water off to the faucet and/or have a plan to keep the area dry for several days. Dry the chip and surrounding area thoroughly. Apply a very thin coat (it's most similar to nail polish). Let dry. (I believe it is 12 hours between coats, but read the bottle.) Apply another thin coat. Let dry. Repeat as many times as necessary until the chip area resembles the rest of the sink or tub.
It took a week in our kitchen because the chip had been there so long, but we were doing a lot of work at the time so not using that one side wasn't a hardship. I put a colander over the chip area with a bright note taped to it and we pulled the sprayer faucet out and laid it in the other side of the sink as a physical reminder. In the bathrooms, I turned the water off to the sinks altogether until it was completely dry. New chips blend better than old chips. The chips in our bathtub were from removing the sliding doors and track, so water wasn't an issue and we weren't using that tub at the time. I was able to put a thicker amount into these holes and let it dry for days, then apply thin coats on the surface as described above. I'm the only one who still sees the holes and that's because I know where they are!
Do I need to be careful when cleaning it? I usually use borax.
