How to Make It
Place chicken, onion, celery, chiles, cilantro, bouillon granules, oregano, cumin, paprika, garlic, bay leaves, water, and 1 teaspoon of the salt in a large pot. Bring to a boil, uncovered, over high. Reduce heat to medium-low, and cook until chicken is very tender, about 30 minutes.
Preheat oven to 375°F. Remove chicken mixture from heat, and strain cooking liquid. Discard cooking liquid (or reserve for another use), and return chicken mixture to pot. Using 2 forks, shred chicken inside pot. Add lime juice and remaining 1 teaspoon salt; toss to coat, and set aside.
Heat a small nonstick skillet over medium-high. Place 1 tortilla in skillet, and toast until just warmed, 15 to 20 seconds per side. Remove to a plate, and repeat with remaining tortillas.
Spoon about 1/4 cup chicken mixture down center of 1 tortilla; roll up. Place tortilla, seam-side down, in a lightly greased 13- x 9-inch baking dish. Repeat with remaining tortillas and chicken mixture.
Pour Green Chile Sauce over enchiladas; sprinkle with cheeses. Bake in preheated oven until cheese is golden brown and sauce is bubbling, about 20 minutes. Remove from oven, and let stand 10 minutes before serving.