Preheat the oven to 400F.
Heat a large, deep skillet over medium-high heat. Once hot, add the oil, and then the chicken. Cook until the chicken is browned on the outside, about 3 minutes.
Turn the heat down to medium and add the peppers, celery, onion, and garlic. Cook until the veggies are softened, but not browned, about 8 minutes, stirring occasionally.
Stir in the chicken broth and salsa verde, and bring up to a simmer. Add the cream cheese and stir until smooth. Turn off the heat and stir in half of the cheddar.
Pour the mixture into a 9 by 11-inch (or equivalent) baking dish. Sprinkle the remaining cheddar and the queso fresco on top. Bake until bubbling throughout, about 10 minutes, and then broil a couple minutes to brown the top.
Serve hot, with any toppings you like.