Whisk together marinade ingredients in a freezer bag and add chicken, turning to coat. Marinade for 2 to 24 hours (the longer the better!).
To easily cook and shred the chicken: Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat until hot and rippling. Add the chicken breasts (and any extra marinade) and cook for 3 to 5 minutes, or until golden brown on one side.
Flip the chicken over, then add 1 cup of chicken broth or water to the skillet. Cover and reduce heat to medium and simmer for 15 to 20 minutes or until chicken is cooked through and tender enough to shred, adding additional chicken broth or water if the liquid evaporates too quickly. Remove chicken from skillet and let rest 5 minutes before shredding.
While the chicken is cooking and resting, prepare burrito filling. Heat 1 tablespoon olive oil in a large skillet. Add onion and carrots and sauté for 4 minutes.
Add celery, green chilies, and garlic and sauté an additional 2 minutes or until carrots are crisp-tender.
Shred chicken and add to filling. Stir in ⅓ cup sour cream and hot sauce to taste until well combined.
Preheat oven to 400 degrees F. Line a baking sheet with foil and add a baking rack on top. Prepare burritos by adding a heaping ½ cup filling to each tortilla (uncooked if using raw tortillas), top with desired amount of cheese and roll up burrito style.
Place burritos on the baking rack and brush both sides lightly with olive oil or spray with nonstick cooking spray. Cook for 18 to 20 minutes or until golden. Broil to desired crispiness, flip over and broil the other side until golden.
Meanwhile, prepare sauce by melting butter in olive oil in a medium saucepan over medium heat. Whisk in flour and cook, stirring constantly for 3 minutes.
Reduce heat to low then gradually whisk in chicken broth. Bring to a boil then reduce heat and simmer 2 to 3 minutes, or until slightly thickened.
Stir in sour cream, ranch seasoning, lime juice, cumin, salt and pepper to taste. Add hot sauce to taste and additional lime juice if desired.
To serve, top burritos with Creamy Lime Ranch Sauce and desired toppings.
