They hunt a domesticated animal? What, they walk up to the tiny pen it’s kept in and shoot it?
No. Wild Caribou are hunted.
Caribou are also (separately) raised on farms. When raised on the farm the same animal is called a reindeer.
Caribou (Rangifer tarandus) live in the arctic tundra, mountain tundra, and northern forests of North America, Russia, and Scandinavia. The world population is about 5 million. Caribou in Alaska are distributed in 32 herds (or populations). A herd uses a calving area that is separate from the calving areas of other herds, but different herds may mix together on winter ranges.
In Europe, caribou are called reindeer, but in Alaska and Canada only the domestic forms are called reindeer. All caribou and reindeer throughout the world are considered to be the same species, but there are 7 subspecies: barrenground (Rangifer tarandus granti), Svalbard (R.t platyrhynchus), European (R.t. tarandus), Finnish forest reindeer (R.t. fennicus), Greenland (R.t. groenlandicus), woodland (R.t. caribou) and Peary (R.t. pearyi). Alaska has only the barren-ground subspecies, but in Canada the barren-ground, woodland, and Peary subspecies are found.
http://www.adfg.state.ak.us/pubs/notebook/biggame/caribou.php