Pet Owner
noun
You know that to 飼う is "to keep a pet." If you're the master that is keeping a pet (飼う), then you are the pet owner.
The reading is the kun'yomi readings for both. You'll need to remember the words 飼う and 主 to be able to remember the reading of this word.
もし犬の飼い主が水疱瘡になったら、その犬も水疱瘡になる可能性はあるんでしょうか。
If a dog’s owner had chickenpox, could the dog get it too?