No, it's not one piece. You can replace just the broken stem. First you have to turn off the water. You can turn it off with the valve nearest your water meter. You might want to turn it off at the valve on top of the water heater, if it's just the hot water side you're working on. (Don't burn yourself on the vent pipe!). Then you still can use the cold water supply while your working. Remove all the shiny stuff from around the stem. At the base of the stem there is a packing nut. They sell special sockets to remove this, but you may be able to get a wrench or socket from your tool box on it. It has to be turned left to remove it. Turn the stem to the left as well, then pull it out. Try to find the manufacturer's name stamped anywhere on the assembly. Take the stem to Home Depot, your local hardware store or a plumbing supplier. Ask them to match you up with a new one and give you all new washers. Twist the new stem tight in the hole, back it off a little, then place the packing washer or new packing rope around the stem. Tighten down the packing nut. Turn the stem full off. Open the water again and check for leaks. If there are none put the rest of the hardware on.