For the enchiladas: Line baking sheet or platter with paper towels. In a small skillet, heat 1 cup of oil until shimmery and hot but not smoking. Lightly fry the tortillas one at a time just until softened, 5 to 10 seconds per side. Transfer to the paper towel-lined pan to drain.
Preheat the oven to 350 F. Lightly coat one of two baking dishes with cooking spray.
Working with one tortilla at a time, dip a tortilla in the red sauce, lightly soaking both sides completely. Place the tortilla in baking dish and arrange about 1 tablespoon of chicken in a line just above the center of the tortilla. Sprinkle over a bit of onion, if desired. Tightly roll up the tortilla and place it at one end of the baking dish. Repeat with all of the tortillas until all the enchiladas are snug in the dish. Use a second baking dish if necessary.
When all of the enchiladas are rolled and snug in a baking dish, pour over any remaining sauce. Sprinkle the cheese over the top and cover the pan(s) with foil. Place the baking dishes in the oven until the cheese is melted and the enchiladas are heated through, 15 to 20 minutes. Remove from the oven. Serve directly from the dish, using a spatula to scoop out the enchiladas. Serve with Mexican rice and refried beans.