Preheat oven to 350 degrees.
In a skillet, brown the onions until soft.
Add in the shredded chicken, taco seasoning, green chilis, and HALF the salsa verde.
Cook over low heat until mixed thoroughly.
Spoon the mixture evenly into the tortillas.
Roll and place in a 9x13 pan with the seam side down.
Continue to do this until your pan is full.
Meanwhile, mix the remaining salsa verde and sour cream in a large bowl until well combined. Slowly add in the milk until the sauce is the consistency that you desire.
Pour the mixture over your rolled tortillas. Sprinkle with both of the cheeses.
Bake for 20 minutes until heated through.
