The route begins on the Bishop Peak trail. The trail has three trailheads the most convenient is located at the end of Highland Drive.
Highland Drive Trailhead: From San Luis Obispo, take the exit for Route 1 (Santa Rosa street). Near the outskirts of town, turn left on Highland Drive and follow it to its end.
Hike along the trail to a junction with the Felsman loop trail. Turn right and head out on this trial for about a half mile. Around here you reach a junction with a faded over trail, this junction is marked with a sign noting the direction of the Felsman Loop trail.
Leave Trail Here
Head up on this faded over trail and quickly turn left toward an even fainter trail.
After a few hundred feet this trail disappears completely, from here head toward this rock outcropping.
Aim For this rock
Once at this outcrop you will have great view of Chumash Peak and a view of the rest of the route.
The route from the outcrop
From here make your way toward the saddle trending slightly left. Head further left and head up the slopes of Chumash Peak. You should eventually intersect an old trail that cuts its way through the brush. From here simply follow this trail to the summit.
This is a relativity short hike, only slightly longer than Bishop Peak. Most people should be done in 2 hours or so.
This description is probably more detailed than necessary. One could probably make it to the summit a number of ways, however the route described here avoids bushwhacking.