Follow the directions for the regular trail of Mt Whitney. After the junction with the John Muir trail, continue up the Whitney trail for about 500m to a wide sandy gully. There is nothing to mark the spot but this is how it looks like from the trail:

and this is the pinnacle across the trail from where the chute is:

Mt Muir is only about 100m higher than the trail, but those are almost vertical meters. If you find the easiest route, it will be all class-3 climbing with scary exposure. The trick is to find the two chimneys that help bypass a chockstone. The first one is located at the far right as you are staring up from the trail.

At the top of that chimney move to the left: find a gap between two stones that you can use to hold yourself and traverse over a very steep boulder. once you are in the second chimney above the chockstone, the rest should be obvious: head to the right and up.

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• Mt Whitney page