This is a Desert Big Horn Sheep, a subspecies of the Big Horn Sheep. The biggest difference between the two is that the desert version can go for longer periods of time without water. According to desertusa.com, they also tend to be smaller and have wider, but flatter horns.
My wife and I found this picture perfect critter posing on a rock perched on the side of the Bright Angel Trail overlooking the Grand Canyon. He and several of his herd crossed over the trail right in front of us while we were making our way back up to the rim. It was a right place right time kind of day.