Season chicken thighs on both sides with salt and pepper. Heat olive oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat.
Brown chicken thighs skin-side down for 4-5 minutes until golden brown. Flip and cook another 3-4 minutes. Remove chicken and set aside.
In the same pot, add sliced onions and cook for 3-4 minutes until softened. Add minced garlic and cook for another minute until fragrant.
Add diced tomatoes, chopped chipotle peppers, adobo sauce, Mexican oregano, and cumin. Stir to combine and cook for 2-3 minutes.
Return chicken to the pot and add chicken broth. The liquid should nearly cover the chicken. Bring to a boil, then reduce heat to low and simmer covered for 25-30 minutes.
Remove chicken from the pot and let cool slightly. Remove and discard skin and bones, then shred the meat using two forks.
Meanwhile, continue simmering the sauce uncovered for 5-10 minutes until slightly thickened. Stir in apple cider vinegar.
Return shredded chicken to the sauce and stir to combine. Taste and adjust seasoning with salt, pepper, or additional adobo sauce as needed.
Serve immediately in warm tortillas, over rice, or in bowls with your favorite toppings.
Notes
Storage tip: Keeps in refrigerator for up to 4 days or freeze for up to 3 months. Reheat gently with a splash of broth. Adjust spice level by adding more or fewer chipotle peppers. For a lighter version, remove chicken skin after cooking.