No according to this link
Hunting is prohibited within Yellowstone National Park boundaries but Big Game, Upland Birds, and various Waterfowl can be hunted in season on public and national forest area land near Park boundaries, and on private land (60 million acres in Montana alone) when owners grant permission.
http://www.yellowstoneparknet.com/summer_recreation/hunting.php
Well, I will add years ago my then BF and I were driving through YNP on a peaceful rd with no one in sight. Suddenly we went around a bend and it was like a parking lot of stopped cars! We look over and there were a bunch of tourists running after a herd of Moose trying to get a picture. The next thing we see are the tourists are running back towards their cars as the Moose started chasing them lol. I will never forget it.
Sorry for the o/t but had to share.