This dinner recipe gets its green coloring from mild green tomatillo salsa, which is widely available. Instead of using four small baking dishes, you can bake one pie in an eight-inch dish.
Preheat oven to 425 degrees. Lightly season chicken on both sides with salt and pepper. Heat a large skillet over medium-high. Add oil and chicken; cook, flipping once, until browned, about 10 minutes. Transfer to a plate and let cool slightly; shred with two forks.
Divide 1/4 cup salsa among four 6-inch, 1 1/2-cup shallow baking dishes. Layer in 12 tortilla quarters, another 1/2 cup salsa, half of shredded chicken, and 3/4 cup cheese, dividing evenly among dishes. Repeat layering. Finish with remaining 12 tortilla quarters, followed by remaining salsa and cheese.
Place dishes on a rimmed baking sheet. Bake until bubbly and tops are golden brown in spots, 15 to 20 minutes. Let cool slightly before serving, with accompaniments.