In a mixing bowl, beat cream cheese with a hand mixer until it's light and fluffy, about 30-60 seconds.
Add in green chiles, lime juice, salt, cumin, chile powder, and cilantro. Stir together. Fold in cooked chicken.
In a separate mixing bowl, stir together sour cream and chile verde until combined.
Place a large spoonful of the chile verde sauce into the bottom of a lightly greased 9x13 pan.
Assemble enchiladas by placing a big scoop if the chicken filling onto the center of a tortilla. Roll up the tortilla, tucking in the ends as you go. Lay it in the prepared 9x13 pan. Repeat with the remaining tortillas.
Pour the remainder of the chile verde sauce over the top of the assembled enchiladas.
Sprinkle the shredded cheese over the enchiladas.
Bake in a 375 degree oven for about 30 minutes, until the cheese is bubbly and lightly browned. Place under the broiler setting for 2-3 minutes for extra browning.