Place the chicken breasts in a pot or Dutch oven and cover with water or chicken broth. Bring to a boil, then reduce heat and simmer until cooked through, about 15-20 minutes. Remove chicken and shred it using two forks. Reserve 1/2 cup of the cooking liquid.
While the chicken cooks, heat the olive oil in a large skillet over medium heat. Add the sliced onion and cook until softened, about 5 minutes. Add the minced garlic and cook for 1 minute more until fragrant.
In a blender, combine the diced tomatoes, reserved cooking liquid, chipotle peppers, adobo sauce, oregano, cumin, and salt. Blend until smooth.
Pour the sauce mixture into the skillet with the onions and garlic. Bring the sauce to a simmer.
Add the shredded chicken to the skillet. Stir to coat the chicken completely with the sauce. Reduce heat to low and let it simmer for 5-10 minutes so the chicken absorbs the flavor.
Warm the tortillas according to package directions.
Serve the chicken tinga in the warm tortillas, topped with your preferred toppings like cotija cheese, avocado, and cilantro.
Notes
For a faster method, use pre-cooked rotisserie chicken and shred it before adding it to the sauce.
If you prefer a thicker sauce, simmer uncovered for an extra 5 minutes after adding the chicken.
This recipe is naturally gluten free if you use corn tortillas.