Don't be put off by the Chimney in the name, there are no chimney moves on the route.
There are many variations to get to the start of the Southeast chimney route itself. Take any of the routes to the top of the balcony or use the first pitch of Exit 99 for a more direct start.
P1- (5.7) The Butterknife
Climb the obvious Butterknife flake, then make moves out to the face on the left continuing up to the manky 1/4 bolts on the face above. Clip the mank and move up to the glorious crack above. Follow this crack for about 50' to your choice of small ledges. Gear anchor.
P2- (5.8-) Pull the roof using great jams and cruise to the top of the balcony on easier ground.
P3- (5.4) Traverse/downclimb/curse your way across the broken ledge system to a nice shady belay with a slung chockstone.
P4- (5.7) Climb up various cracks and face features to a gear belay near the base of the "chimney".
P5- (5.7) Get your jam on up the various cracks to the "notch" at the top. There is a bolted anchor just on the other side of the notch. Enjoy the views of the Pioneer Range. Leave that heavy trad rack clipped to the anchor for the last pitch. You can get it on the way down.
P6- (5.8) Climb to the top of the block above the belay and peer left around the edge of the south face. There is a bolt. Clip it and down climb a few feet. Commit to the face, this is the crux. Once on the face follow the bolts to the "top". Bolted anchor.
Either rap from this anchor to the ground or follow the ridgeline to the true summit (5.2).
A 70M just barely gets you down. Tie the ends!
Nuts, 2x cams to #3, a 4 and 5 are really nice, but probably not needed.