Possibly a contaminated faucet tip aerator, and the faucet tip.
Remove the aerator without losing parts down the drain and put it in a glass of water with a cap of bleach for 20-30 minutes. Watch the chrome doesn't start coming off. Then rinse it with clear water an reassemble.
While soaking the aerator, hold the glass up to immerse the faucet tip for as long as possible, then rest and repeat etc..
It could be the overflow drain of the sink is causing the odor. They are found up under the rim or in the rim of the front edge of the sink.