Bring the Tomato-Chili Sauce to a simmer over medium heat in a large pot.
Heat the oil in a large nonstick skillet over medium heat. Crack the eggs into the pan and cook, covered, to the desired doneness, 2 to 4 minutes for slightly runny sunny-side-up eggs.
Meanwhile, add the tortilla chips to the sauce and stir to coat. Top with the eggs, cheese, jalapeños, cilantro, and cayenne.