From the Nisqually (southwest) entrance to Mt. Rainier National Park, follow the road ~7mi to Longmire. Turn right at the entrance near the Longmire Wilderness Information Center and drive through the housing area for the park employees, crossing a narrow one-lane suspension bridge over the Nisqually River. Locate the start of the Eagle Peak Trail
on the left/east side of the road, a short distance past the bridge. Alternately you can park at the Wilderness Info Center and hike in.
Follow the Eagle Peak trail upwards from Longmire (~2800') on a well-graded and well-maintained series of switchbacks for ~3.6mi to the saddle between Eagle Peak
and Chutla Peak. Elevation gain to this saddle is ~2800'.
From the saddle, head south along an obvious user trail which seems to dead-end shortly atop a steep cliff. Back up a few feet and look to the right to locate a user trail concealed by the trees/bushes that drops down throug the trees to descend below the cliff face. Continue along the ridge following the user-trail up and down - bypassing the occasional high point along the ridge and making your way towards Chutla's summit. The route does not require any gear, but extensive use of the "veggie-belay" (e.g. roots & branches) is probably recommended. There is a bit of slightly exposed rock scrambling along the way (class 3-4).
For primo summit photos on a good day -- have folks stay on the summit and walk down the southern ridge a short distance for terrific background views of Mt. Rainier.
Chutla's probably easy enough if it's dry, but you may like a handline through a couple of sections if it's wet. Ice axe and crampons, of course, in the early season. Beware of a cornice build-up along the ridge -- in winter it's probably easier to climb a snow gully almost directly up to the summit rather than coming from the saddle.