This is not a trail run. It's a scramble. Unless you can defy gravity, no.
From the lowest point of the connector between Kit Carson and Challenger Peaks (Kit Carson Trail
), find a small, steep gully/rock chimney. Descend a short distance and start scrambling up it. The rock is excellent, but this is very steep and exposed. Climb up about a hundred feet before coming to some easier terrain. Continue to scramble up and to the right before reaching a flat area and a short dirt path. Continue along the path, jumping across a 3-4 ft gap in the trail (a small "leap of faith"). Continue along the trail toward the obvious summit, scrambling briefly on some easy terrain here and there. The hardest part of this trail is the initial scramble, so it's pretty easy once you're up that.
Up this high, there are marmots and pika, but not much else.