Preheat oven to 350 degrees F (175 degrees C).

Cook manicotti shells according to package directions until al dente.

In a large bowl, combine cooked cubed chicken, 1 1/2 cups shredded Monterey Jack cheese, shredded cheddar cheese, sour cream, 1/2 of the chopped onion, and 1/2 of the chopped green chilies.

In a separate bowl, combine cream of chicken soup, salsa, milk, remaining onion, and remaining green chilies to make the sauce.

Spread half of the sauce mixture evenly in a 13 x 9 inch casserole dish.

Stuff each cooked manicotti shell with the chicken and cheese mixture.

Place the stuffed manicotti shells on top of the sauce in the casserole dish.

Pour the remaining sauce over the stuffed manicotti.

Cover the casserole dish with aluminum foil.

Bake in the preheated oven for 30 minutes.

Remove the foil and sprinkle the remaining 1/2 cup of Monterey Jack cheese over the top.

Bake uncovered for an additional 10 minutes, or until the cheese is melted and bubbly and the manicotti is heated through.