How do you remove calcium build up from a chlorinator?

You can get the correct material to do this from your pool shop. acid removes calcium, however I wouldn't guaranty that it wont destroy the chlorinator. A: if the device is more than 3 yrs old - replace it. You could go thru and refurbish it but this takes someone with knowledge of what the chemicals you have to use and when and how much. However, as I read your question it makes me think that you are using a liquid feed chlorine feeder. You definitely do not want to mix different types of chemicals together in this situation. YOU COULD GET YOURSELF BADLY IN INJURED AND END UP IN THE HOSPITAL OR WORSE. CHLORINE GAS IS NOT SOMETHING YOU WANT TO DEAL WITH. YOU COULD END UP WITH THE HASMAT TEAM EVACUATING YOUR NEIGHBORS. Have a pool service tech do it for you at least once or twice and observe to see of you actually want to tackle such a job.

You should not be getting calcium buildup in a tablet feeder. BEWARE: CHLORINE AND MURIATIC ACID DO NOT MIX WELL. THEY ARE NOT COMPATIBLE k