In a small heavy saucepan, cook the butter and flour over medium high heat, whisking, 1 minute.
Pour in the milk and 1/4 teaspoon each salt and pepper and bring to a boil, whisking constantly.
Boil 5 minutes, then remove from the heat and whisk in the queso freso.
Season the sauce with salt and pepper to taste.
Reserve the bechamel.
In a large heavy skillet, heat the oil over medium high heat until hot, then stir in the on-ion, garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper and cook, stirring occasionally, until golden, about 6 minutes.
Stir in the chicken and chiles along with their juices, and cook until the chicken is cooked and the liquid is evaporates, about 5 minutes.
Season the filling with salt and pepper to taste.
Preheat the oven to 350F.
Divide the filling between the tortillas.
Roll each tortilla into a cylinder and place, side-by-side in a baking dish.
Pour the bechamel over the tortillas and sprinkle with the cheddar cheese.
Bake the enchiladas until the filling is hot and the cheese is melted, about 10 minutes.