Preheat the oven to 350 degrees F. Combine the chicken and onion in a bowl and mix gently. Combine the enchilada sauce and sour cream in another bowl and mix until smooth. Transfer 3/4 cup of the enchilada sauce mixture to the bowl with the chicken. Mix well. Heat a small non-stick skillet over medium heat. Add the tortillas, one at a time, turning to heat on both sides. Transfer the tortillas to paper toweling and cover lightly to keep warm. Spread some of the enchilada sauce in the bottom of a 9x13-inch baking dish (just enough to cover the bottom lightly). Add about 1/3 cup of the chicken mixture in a line down the center of each tortilla. Roll the tortillas up around the filling and place the tortillas, seam-side down, in a single layer in the baking dish. Evenly top the rolled tortillas with the remaining enchilada sauce mixture. Sprinkle evenly with the Monterey Jack and Cheddar cheese. Place the enchiladas in the oven and bake at 350 degrees F for 20-30 minutes or until the cheese is melted and the sauce is bubbly. Remove the enchiladas from the oven and serve immediately.