The sink is in the powder room on the main floor of our house. When I turn the water on it is fine for a few seconds then it smells horribly for about 3-4 more seconds then it is back to normal. It is the only water in the house that smells, so it's not the water coming into the house. I checked the drain and trap and they are clean and have no odor. I poured water from my kitchen sink down the drain of the powder room and didn't get the odor. So I know the odor isn't coming from the drain or overflow. I plugged the drain and ran the water for about ten seconds and once again got the smelly water. The water in the basin did continue to smell, so I know it is the water coming out of the faucet that smells bad, and not the drain. It doesn't seem to matter if I use hot or cold water. The sink is the closest one to the water heater, if that could make a difference. I'm just not sure where to go from here.
A rotten egg smell in water is usually from high sulfer content in the water. Not unheard of in very hard water. Where it could possibly be coming from in the pipe perplexes me though. The fact that it only comes out one faucet is odd. If both the hot and cold smell bad at only that faucet and no other than the problem must be in the faucet itself, since if it was in the water heater all the hot water in the house would smell and the hot and cold pipes are 2 different pipes until they get passed the supply lines below the sink.
I would shut off the water below the sink, open the valves to drain out any water that might be sitting in the pipe and then see if the faucet outlet itself smells odd. If there is a screen at the mouth of the faucet remove it and see if there is debris inside.
This is hardly an answer but I'd target the faucet or something trapped inside it as the problem.
Love to hear what the problem ends up being.
I have a similar issue, and a guy at Lowes told me that a possible reason for the issue only occurring at the one faucet could be corroded pipes.
My water is absolutely terrible (as you can read over here) but with a massive amount of filtering it comes out fine, except the one faucet. He said that once the bacteria gets past my filters, it takes up a home in the corroded section of pipe. He recommended finding and removing the corroded section since even if I could get it clean, as soon as any more bacteria got through it would cause the same issue.
This is a common problem in some areas with high sulfur well water. The issue is that iron fixing bacteria takes up residence in the well, slowly corroding steel parts and generating hydrogen sulfide, which smells like rotten eggs. Often the issue is only severe on the hot water side of a system because the bacteria loves 125F-140F warm water in the hot water heater, thriving there and making a very odoriferous problem.
Chlorinating the system is recommended as a fix by many plumbers. Unfortunately, this is usually a very temporary solution. The bacteria which causes the odor is endemic in the well and after the system is chemically sanitized then the bacteria simply re-established itself where it was, being re-introduced by the well water. Fortunately this particular bacteria is not toxic.
If the problem is really noticeable only on the hot water side (also extending into the cold water line near the water heater), then a good permanent fix is to increase the hot water heater temperature to about 160F, which will kill all the bacteria on an ongoing basis. This is a scalding hot temperature, so a mixing/tempering valve must also be installed, bringing the water back below scalding temperatures as the water is dispensed. This arrangement is also sometimes known as a "hot water extender" because it increases the hot water capacity on standby. Unfortunately, some hot water heaters cannot be set this hot. Others require a "performance kit" or other accessory.
The only other permanent fix I know of is to install a chlorinating system or something similar which continuously injects chemical sanitizer into the water as it is pumped out of the ground.