I was on the NE Buttress of Chair this weekend linking up patches of vertical ice and frozen Heather clumps. The N. Face IS NOT in... mostly bare rock.
We had do some 5th class just to get up to the notch on above the "thumb tack" basin. There was one other party that turned around after witnessing us use gear on the approach
The climbing was spectacular... very exposed but also run out. A real classic mixed climb. With the conditions we found and the variations that we did I would give it Grade III AI 3 5.6 (Left car at 8:30, climbing at 11:00 AM summit at 4:00 PM back at car at 7:00 PM)
Not super sustained.. you had no hands rests after 15 feet of climbing or so... the gear was sparce though. The only gear we used was a #1 & .5 camalot, a #6 nut and 4 kbs (some tied off). Oh, and slings for the occasional krumholtz.
Climb the rightward slanting gully (5th class) to some blue slings. From there head right and up onto the ridge proper. From there head towards a Yellow sling a full rope up and right. From there look for a cool band of water ice cascading over some technical terrain... this is the AI3 section for about 30+ feet... there are some trees atop this cliff. from the trees angle right along the ridge using trees for anchors... this is class 3/4 ground (50 - 60 degree snow with good anchors) You should end up in a notch after 300-400 feet. The summit is another rope length along the ridge to your right. The descent is straight ahead. Head down the gully by down climbing. You will end up at a col above the exit gully. You should see some anchors (yellow and blue super tape). Use these to rap into the gully (recommend 2 60 m ropes... can be made with 5 single rope raps... some of the anchors look dubious).