Begin at the Meyson Lakes trailhead which is located at the bottom of Whitney portal. From the trail head, you will hike along some paved roads, between assorted cabins and then trail all the way up toward Meyson Lake. Not far off is a sign infroming your entering of the Inyo wilderness area. The trail stays high on the north side of Meyson Creek and the first lake with nice camping is Grass Lake. No need to camp there, follow the sign to Camp Lake - if camping, most choose to stay here. If you want, you can continue hiking ~15 mins further up to Meyson Lake and camp there but the spots are not as nice and the landscapes are not as beautiful (subjective I guess).
From Grass Lake or Meyson Lake, hike up into the snow field just below the prominent snow chute to the north of the East Buttress. If late spring/early summer, it is best to get on an off the snow before the sun hits it for too long or else it will be a long slog up soft snow. Asend the couloir. About 2/3rds up, the couloir splits into a "Y": the left is more direct and easier; the right side is slightly steeper yet tops out lower on the ridge. Either way, upon gaining the ridge, turn left and head up the easy class 2 rocks to the summit. There may be some "light" class 3 sections but all in all the hardest part of the climb is completed after reaching the ridge.
Crampons and an ice axe are likely required but because the couloir is not too steep, a skilled climber could likely ascend easier using poles in early season in place of an axe proved s/he never needs to go into self-arrest. If done in fall as an ice climb, neccessary ice climbing gear is needed.
I am 100% certain this route has been climbed many times previously but I could not find any description of it in Secor. If anyone can add anything to its history or its original name (if it has such) that would be great. I just labled it Birkenhead because that is Irvine's home town in England.
*** update: I found in my Eastern Sierra Ice Climbing Mini-Guide a reference to this route; it was described as the "East Couloir" and stated it often freezes into a nice 30-degree ice climb. I now renamed the route East Couloir from Birkenhead chute.