I am a mechanic, the serpentine is what they will be taking off to get the water pump out, not the timing chain (or belt depending on the car). The chain times the pinion, rods, and heads in a particular order. The serpentine belt, or accessory belt, operates water pumps, A/C compressor, power steering pump, harmonic balancer, and puller/tensioner. Depending on your vehicle, whether you went to the dealer (“sounds” like a dealership price), or a mechanic shop will make all the difference in price. Water pump will range and so will the labor. I say look around, if the price is around the same everywhere, you have a difficult car. If it drops quiet a bit, then is is the shop. Unless it is complicated work, like engine rebuilding or transmission work, don’t go to the dealership. It is there job to make you pay as much as you can.