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When ready to cook, start Traeger on Smoke with lid open until fire is established (4-5 minutes). Increase the temperature to 350 degrees F and preheat with lid closed for 10 to 15 minutes.
Rub olive oil over chicken and season with salt and pepper. Place chicken directly on grill grate and cook for 1 hour or until chicken reaches an internal temperature of 165 degrees F. Remove from grill and let rest for 10 minutes.
Shred the chicken off the bone with a fork and set aside.
In large skillet, heat oil over medium-high heat. Add onion and saute for 3 minutes, stirring occasionally.
Add green chiles, and season with salt and pepper. Saute for 6-8 minutes, stirring occasionally. Remove from heat and combine shredded chicken to mixture.
To assemble the enchiladas, set up an assembly line including: tortillas, enchilada sauce, beans, chicken mixture, and cheese. Lay out a tortilla and spread two tablespoons of sauce over the surface of the tortilla. Add beans in a line down the middle of the tortilla, then add a spoonful of the chicken mixture and sprinkle with 1/3 cup cheese.
Roll up tortilla and place in a greased 9 x 13-inch baking dish. Repeat with remaining ingredients.
Spread the remaining enchilada sauce on top of the tortillas, and sprinkle on remaining shredded cheese.
Place baking dish directly on grill still at 350 degrees F, close lid and cook uncovered for 20 minutes.
Remove from oven and serve immediately. Garnished with sour cream and chopped fresh cilantro. Enjoy!