Preheat the oven to 400°F (200°C).
Pour about 1/4 cup of the enchilada sauce into the bottom of a 9x13-inch baking dish and spread to lightly coat the base.
In a mixing bowl, combine the scrambled eggs, shredded or cubed chicken, chopped green chiles, and half of the remaining enchilada sauce; stir until evenly mixed.
Place half of the tortilla chips in an even layer in the prepared dish.
Top the chips with half of the chicken-egg mixture, half of the Queso fresco, half of the Monterey Jack, a drizzle of remaining sauce, and about half of the Mexican crema.
Repeat with a second layer: remaining chips, remaining chicken mixture, the rest of both cheeses, and the remaining sauce (reserve extra crema for garnish).
Bake uncovered for about 20 minutes, or until heated through and the cheese is melted and bubbling.
Remove from the oven and garnish with additional Mexican crema, chopped cilantro, and pico de gallo to taste; serve immediately.
