In a pot, cook the grits according to package instructions. (I used 1 cup grits to 3 cups water with 1/2 teaspoon salt.) When the grits are almost done, add milk, chiles and cheese. Cook an additional 10 minutes until the cheese is melted throughout the grits.
In a frying pan, add oil and allow the pan to heat up. Cook 4 fried eggs, sunny side up. Use salt and pepper to taste.
Spread grits on a plate and top with an egg. Sprinkle chives on top. Serve hot.