Heat the jar of salsa verde in a pan over medium heat. Remove the pan from the heat and stir in the sour cream and cilantro. Set aside about ½ cup of the sauce.
Stir the shredded chicken and ½ cup of the cheese into the sauce that has not been set aside.
Heat the oven to 350 degrees. Spread a little of the reserved sauce on the bottom of a 9x13 baking dish. Add about ¼ cup of the chicken filling to each tortilla and roll. Repeat. Add the filled tortillas, seam-side down, next to each other in the dish.
Add the rest of the reserved sauce on to the tortillas. Sprinkle the remaining cheese on top.
Add aluminum foil on top of the dish before placing it in the oven. Bake until the enchiladas are heated through, approximately 15 minutes.
Remove the aluminum foil and bake 5-10 minutes longer, or until the cheese on top is melted.
Serve with extra cilantro and sour cream.