Heat oil in a large skillet. Add onion; saute until softened, about 5 or 6 minutes. Stir in tomatoes, chili powder, oregano, salt and pepper. Simmer for 10 to 12 minutes to blend flavours, stirring occasionally.
One at a time, break eggs into a small bowl and then into the sauce. Cover skillet and cook over medium heat until eggs are done as desired, about 6 minutes.
Serve over rice, tortillas or toast. Garnish with cilantro if desired.