Heat a large dutch oven over high heat for several minutes.  Add 2 tbsp of the oil and when it is shimmering hot, add the chicken thighs. Season well with salt and pepper and cook, undisturbed, until well browned, about 3 minutes (when they're ready to flip, they will lift easily without tearing). Flip and cook until opaque, about 3 minutes more.  Transfer to a bowl.

Heat remaining oil in same dutch oven over high heat and add peppers, onions and jalapeno. Season well with salt. Cook, stirring fairly frequently, until onions are soft and deep golden, and peppers are charring in spots, about 30 minutes. Add garlic and cook until fragrant, a few minutes more. Taste and add more salt as needed.

Cut or tear chicken into bite-sized pieces and return them to the pot along with any accumulated juices.  Cook just until chicken is reheated, a minute or two, then serve with tortillas and desired toppings.