If camping at the Glacier Gorge Backcountry site #39, walk the additional 1.6 miles up the trail south to Black Lake. From Black Lake, the easier approach takes you along the east side of the lake on a trail, and begins gaining elevation to the east below steep cliffs and two smaller streams to about 11,000 ft. where you can then head south at a fork and make a gradual arching turn to the west gaining enough elevation to cross a little below (north of) Frozen lake. If snows have melted, you'll find a trail for this section. Views of "The Spearhead" dominate this portion of your hike. From just below Frozen lake, continue west and locate the ramp through the cliffs SE of the McHenry's summit that allows non-technical access to the south side of the ridge that connects McHenrys and Chiefs Head. This is called "Stone Man Pass." Progress above Black Lake is made more difficult by sections of low-growing conifers and deciduous shrubs.
Stone Man Pass is a break in the otherwise formidable cliffs that ring this basin. The route follows a steeply sloping ramp for over 400 vertical feet through the cliffs on rock, gravel and scree. In early season, this may/will be snow-covered and will require ice axes for safety. This section we would rate at Class 2+.
Once through the pass, you'll have two basic choices. Either attempt to follow the ridgeline S, then SE to the Chiefs Head summit or drop down about 500 feet into the basin above Lake Powell and then contour until you feel you can more easily ascend back up toward the upper portion of the NW ridge of Chiefs Head, several hundred feet below the summit. The traverse across the Lake Powell basin will be tedious on very large boulders requiring extensive rock-hopping. Following the ridge has multiple problems resulting in a Class 3 rating. See a link provided below for a report on navigating this NW ridge. So pick your poison. If taking the contour route above Lake Powell, look for a couple of couloirs that lead up through the rock bands and take you back toward the NW ridge of Chiefs Head. This will bring you onto a large, west-sloping tundra plateau. As you progress back toward the west ridge and follow it toward the summit, the terrain will change to large rock blocks requiring a fair amount of boulder-hopping. The last half mile seems never-ending.
The summit offers a splendid view looking back down Glacier Gorge and of Longs Peak, Mt. Meeker, Pagoda and McHenrys Peak. The view of the SW side of Longs is inspiring & impressive.
For the descent, retrace whatever route you choose back to Stone Man Pass. Here, decide if you want to continue on to McHenrys Peak. If not, descend the steep ramp north from Stone Man Pass. Once below the ramp, an alternate route down leads toward a tundra bench at 11,500 feet almost directly west of Black Lake. From the bench, walk north some more, contouring through dense scrub, following natural ramps and benches to a crack system in the rocks that allows access through a minor cliff band. Once through the cliff, it's an easy but very steep descent back to Black Lake where you can pick back up the well-defined trail out.
Chiefs Head can also be climbed from the Wild Basin side. There are numerous internet reports on approaching it from that direction. Done this way, it's often combined with Pagoda and/or Mt. Alice. The overall mileage is significantly longer than the Stone Man approach.
Links to other information, routes & trip reports for this peak that may be helpful.