Broil chiles, turning once or twice, until skins are charred all over. Let sit until cool enough to handle, then peel skins and discard stems and seeds. Dice chiles.
Preheat oven to 350°. In a 3- or 4-quart pan over high heat, bring chicken stock to a boil. Add grits, reduce heat to medium, and stir until stock is absorbed, 5 to 6 minutes. Stir in butter, cheese, and chiles.
In a small bowl, whisk 1/2 cup of the cooked grits into the beaten eggs. When blended, stir this mixture back into the saucepan with the rest of the grits. Pour mixture into a greased 2-quart casserole. Bake until just set, 25 to 30 minutes.
Note: Nutritional analysis is per serving.