According to
this article it appears to be the Hemlock chair at Boyne Mountain. It started life as the Dollar Lift in Sun Valley in 1936 and was one of two lifts installed that year. At the time, there were no other chairlifts in the world, so that would make it the oldest.
It was sold to Boyne in 1948, and later upgraded from a single to a double. They also replaced the wooden lift towers and motors along the way so there's a bit of "grandfather's axe" going on here. (i.e. "This is my grandfather's axe. I've replaced the axehead twice and the handle four times, but it's still my grandfather's axe.") But the terminals and bullwheels are still the original. Is that enough original equipment left to make it count as the oldest?
The chair is still operational, but they only run it on high traffic days since there's a high-speed six-pack that runs parallel to it.