Preheat oven to 425 F.
In a 10 inch nonstick pan, heat oil until smoking. Add onions and celery and cook until very soft, about 10 to 12 minutes. Add eggs, thyme and salt and pepper and continue cooking on top of stove until just starting to set, about 6 to 7 minutes. Place in oven and cook until set, about 8 to 9 more minutes. Remove, flip out onto plate and cut into wedges to serve with chicken.