Season the chicken thighs lightly with salt. In a large skillet, heat the olive oil over medium heat. Sizzle the chicken until lightly browned on both sides, about 4 minutes per side. Remove and set aside.
In the same skillet, add the onion and a pinch of salt. Cook until soft and slightly caramelized, about 5 minutes. Add the garlic and stir for about 30 seconds until fragrant.
Return the chicken to the pot. Pour in the chicken broth, chipotle peppers, and tomato sauce. Stir in the cumin and oregano. Bring to a gentle simmer.
Reduce heat to low, cover, and let simmer for 15–20 minutes, or until the chicken is cooked through and tender. Remove the chicken and shred it with two forks. Return the shredded meat to the sauce and toss to coat.
Taste and adjust salt if needed. If you like more heat, add a bit more minced chipotle or a splash of adobo sauce.
Warm the tortillas in a dry skillet or wrapped in a clean cloth in the oven at 350°F (175°C) for about 5 minutes until pliable.
To serve, spoon chicken tinga into warm tortillas. Top with fresh cilantro, red onion, a squeeze of lime, and cheese if using.