Mount Chamberlin is a 13er located Southwest of Mount Whitney, in Sequoia National Park. It is on the SPS list. It does not receive many visits, and when it does it is usually in conjunction with ascents of Mount Newcomb, Mount Pickering, Joe Devel Peak and Mount Guyot, or a subset of these peaks.
Hike over New Army Pass or Cottonwood Pass. From there, there are three options: 1) Head for the Perrin Creek drainage (to climb easy sand/talus routes up the West or South slopes of Mount Chamberlin). 2) Head up to Miter Basin and climb Mount Chamberlin by traversing from Mount Newcomb. This option will likely involve some 3rd class climbing. 3) Head up to Crabtree Lakes. This affords access to the steep Northern aspect of Chamberlin, featuring several technical routes.
There are several ascent options:
Overnight trips in the Inyo National Forest and Sequoia National Park require wilderness permits. Consult recreation.gov for further information.
Chamberlin can be climbed any time of the year, conditions and access to the trailhead permitting.
There are excellent options for a basecamp in the Perrin Creek drainage, at Crabtree Lakes or in Miter Basin.