Preheat oven to 350 degrees and place the chicken breasts on a sheet pan skin side up. Rub with olive oil and sprinkle with salt and pepper. Roast for 35-40 minutes, until cooked through.
Cool chicken and take off the skin. Remove meat from bones and shred with a fork. (Or if using supermarket rotisserie chicken, remove skin from chicken and meat from bones. Tear or slice into approximately 2 inch strips.)
Place chicken in bowl with cream cheese, onions, chilies and spice. Stir to combine.
Spray a casserole dish or disposable foil baking pan thoroughly with cooking spray. Pour one-third of enchilada sauce in the bottom of the pan.
Spoon 2 tablespoons of chicken filling into each tortilla and roll tightly. Place seam side down in baking dish. Cover with remaining enchilada sauce and then top with cheese. Cover with foil.
If making ahead, refrigerate until 40 minutes before you'd like to serve. Bake at 350 degrees for 30 minutes (if room temp) or 40 minutes (if chilled) covered with foil.