Water (hot and cold) run fine in all 3 bathrooms. My kitchen sink is another story. The cold water pressure is fine but, when you switch to hot water, the pressure drops to a trickle. Any ideas ?

Your hot water line could not accommodate an extra kinchen sink. You could increase your pipe size or install a circulating loop and pump to circulate your hot water back to water heater and reheat. That means equal pressure to all outlets. This is applicable if your are using a tank type water heater.

The most likely thing is a build up of crud in the line. Shut the water off at at the stop under the sink. Pry the cap off the handle, remove the screw, and then the handle. There should be a nut. Remove it and you can pull the cartridge out. Hold a towel over the opening, and give it a shot of water from the stop. You may need to rinse some crud off the cartridge before putting it back together.