1. Place chicken, 1/2 of the onion, the garlic, and 1/4 teaspoon salt in a medium saucepan. Add enough water to cover by at least 1 inch. Bring to a boil, and then reduce heat. Simmer until chicken is cooked through, 18 to 22 minutes. Reserve 3/4 cup of the cooking liquid; set aside.

2. Let chicken cool on a plate. When cool enough to handle, shred (discard bones). Coarsely chop 1/2 cup cilantro, and toss with chicken.

3. Preheat broiler, with the rack about 6 inches from heat source. Broil tomatillos and chiles on a rimmed baking sheet, rotating them as they blacken, 10 to 12 minutes. Let cool. Remove the blackened skins, stems, ribs, and seeds (optional) from chiles. Reduce oven temperature to 375 degrees.

4. Coarsely puree tomatillos and chile flesh in a blender with remaining 1/4 teaspoon salt, remaining 1 1/2 cups cilantro, and reserved 3/4 cup cooking liquid. Transfer salsa to a large bowl.

5. Using tongs, toast tortillas over an open flame of a gas stove, 5 to 10 seconds per side. (Or heat the tortillas in a skillet over high heat.)

6. Dip 1 tortilla into salsa to coat lightly. Place 1/3 cup chicken on half of tortilla. Sprinkle 2 tablespoons cheese on top, and roll up. Place it seam side down in a 9-by-13-inch baking dish. Repeat to make more enchiladas, lining them up snugly in dish. Spoon remaining salsa on top, and bake until heated through, about 20 minutes.

7. Slice remaining onion, and scatter over top; drizzle with sour cream.