This is an obvious, direct approach to the summit of Rockchuck Peak, with many airy perches and spectacular views. However, it involves some bushwhacking, exposure, tricky downclimbing, and Class 4 conditions that can easily become Class 5. Although it is an enjoyable route, it is not a mere scramble and most certainly not what you would take your newbie partner on to give him or her a taste of the alpine world.
Just before the road becomes one-way-only as it skirts Jenny Lake, take the well-signed spur for String Lake and park at the Leigh Lake TH.
One-way distance is about 4 miles, with approximately 4400' of elevation gain from car to summit, but some ups and downs along the way may add another couple hundred feet or so. The first 1.6 mi is by trail and gains only about 400'. Yeah, it's a steep route. It's the Tetons, after all; that vertical rise from the floor of Jackson Hole is one of the Earth's greatest sights, but it's not one of its greatest things to climb.
From the trailhead, hike north to Leigh Lake, making a bridged crossing of its outlet just before reaching the lake itself. The trail begins its climb shortly after this crossing. When you reach a signed junction at almost 7200', head right for Paintbrush Canyon. Shortly after that, look for a semi-open area presenting fairly easy access (in terms of terrain features) to the northeast ridge of Rockchuck Peak. Hike up steep meadows to gain the ridge and then do some easy bushwhacking up the wooded ridge. The trees all but peter out at around 9200', and there are outstanding views for the rest of the way.
Alternately, you can stay on the trail and gain the ridge where it meets the trail a short distance northwest.
After things open up, you soon get to the more challenging portions of the route. The ridge has several gendarmes almost all the way to the summit. Usually, it is easy to climb up these gendarmes, but they frequently present sheer faces and nasty drops on their other sides, forcing Class 4 or 5 downclimbing or backtracking. Sometimes, though, it is possible to go from one to the next and keep the fun scrambling and the great views going. When it becomes necessary to bypass a gendarme, do so on the left. This often means giving back some gained elevation, though.
A disciplined, sensible climber will simply stay to the left of the gendarmes the whole way and save a good deal of time and effort. I knew this but could not resist tackling several of the gendarmes. No regrets.
Past the last of the gendarmes, either regain the ridge and follow it to the summit or wander across the face below the summit and scramble up that way. The latter is what I did, so I cannot reliably report on the finish of the ridge; from below, it looked
difficult, but from above, it did not. Remember-- that is how it looked
On the face, you may see a steep, snow-filled couloir seeming to lead directly to the summit. This couloir looked way too steep for a glissade on the way back down, and I chose not to climb it because it seemed that crampons would be needed, and mine had been left behind. If you want to climb this couloir, I strongly recommend using crampons and wouldn't be surprised if it is steep enough to require more technical gear than that.
What I did was scramble up the face to the right of the couloir (Class 3 and 4) and then walk across the head of the couloir before the short final scramble to the summit.
If the route is snow-free, and it should be in summer, all you need are sticky soles, nerve, and patience.
However, if you plan to descend via the east slopes, you will need at least an ice axe.