The Pellissier Gully is on the east side of the Pointe Lachenal, so you can't see it from the Aiguille du Midi. You can find the gully to the left of the rock route Marylene. This means you have to go past the big snowy couloir, and go up the next snowfield. The right branch is the Cecchinel-Jager, the left being the Pellissier Gully.
Start in Chamonix by taking the lift to the Aiguille du Midi. Exit the tunnel, possibly spend the night in the Abri Simmond bivouac or at the Cosmiques hut. Cross the Vallee Blanche in easterly direction, passing the north face of the Pointe Lachenal on the left. Go right roung the Pointe Lachenal (towards Italy) and pick your gully.
First go up the snow slope below the gully. Take the left branch.
P1, this is where the ice section starts. Some nicely angled ice (65°) leads you to an obvious block in the middle of the gully for a belay.
P2, above this block are two branches, take the left one (75°, M4).
P3, about 15 m gradually steepening ice (up to 85°), then a snow slope. There is a belay directly above the ice, but keep on going. There is another belay higher up in a niche on the left.
P4, 15 m of mixed climbing. Then a (possible) intermediate belay. Take it, it makes belaying for the rest of the pitch easier. From here it's more rock climbing (5b/c), with an interesting step from the right to the left branch. Finish at a small coll.
We continued up the snow slope only to find another fine pitch, not mentioned in our guide book.
P5, leftward slanting mixed pitch (50 m, 70°). Good belay at the top on a rock needle (just sling it). From here about 30 m of easy mixed climbing to the top.
Descend the north face easely.
Double rope (60 m), a few short icescrews, a rack of camelots (up to 3) and some pitons.