Preheat your oven to 350°F (175°C) and lightly grease a 9x13 inch casserole dish.
In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add the chicken and cook for about 8-10 minutes per side until cooked through; remove from the skillet and shred the chicken with two forks.
In the same skillet, sauté the chopped onion, minced garlic, and diced zucchini in the remaining olive oil over medium heat for about 5-7 minutes until the vegetables are tender.
In a large bowl, combine the shredded chicken with the sautéed vegetables, softened cream cheese, sour cream, and half of the enchilada sauce until well mixed.
Spread a layer of the remaining enchilada sauce on the bottom of the prepared dish, then place 4 tortillas side by side on the sauce. Spoon half of the chicken mixture over the tortillas and top with a sprinkle of cheese.
Repeat the layers with the remaining tortillas, chicken mixture, and enchilada sauce, finishing with a generous topping of cheese.
Cover the dish with foil and bake for 30 minutes, then uncover and bake for another 10-15 minutes until the cheese is bubbly and golden.
Allow the enchiladas to rest for 5-10 minutes before slicing and serving.