The 270 will certainly do the job. Coyote2 is right though... SHOT PLACEMENT.
I'd be looking into Fail Safe, Swift-A-Frame, or Trophy Bonded Bear Claw bullets. Don't go cheap on the one item that will get the job done! 150gr bullets are the start point. For handloaders, look at Hawk bullets, they're available in heavier weights. 160gr will give better sectional densities when you can find the heavy weights.