Heat oil in a skillet over medium heat, then cook garlic until fragrant, about 1 minute.
Stir in the salsa verde and cook for 1 minute. Remove the skillet from the heat, and then stir in the sour cream and cilantro. Taste for seasoning, adjusting with salt, pepper, or more sour cream if the sauce is too spicy.
Set aside about 1 cup of the sauce for assembling the enchiladas.
Stir the shredded chicken and half of the cheese into the sauce in the skillet.
Heat the oven to 350° F (177° C). Grease a 2-quart baking dish and spread a little reserved sauce on the bottom. Add about ⅓ cup of the chicken filling to the middle of each tortilla and roll into a cylinder.
Repeat, lining up tortillas, seam-side down, tightly in the dish. Spread the reserved sauce over the tortillas and sprinkle with the remaining cheese.
Cover the dish with aluminum foil and place in the oven. Bake until heated through, about 15 minutes. Remove the foil and bake 10 minutes longer, until the cheese melts. Serve with cilantro on top.
