Place chicken in a bowl, add chipotle, and salt and toss until meat is well coated. Set aside.
Heat 1 teaspoon of the oil in a large frying pan over medium-high heat. When it smokes, add half of chicken and cook until golden brown on both sides, about 1 to 2 minutes per side. Remove to a plate and, return pan to stove, add 1 more teaspoon of the oil, and repeat with second batch.
Add remaining 1 teaspoon of the oil, add onion and garlic and cook until golden and soft, about 2 minutes. Add peppers and cook until softened and golden brown, about 3 to 5 minutes.
Return chicken and any accumulated juices to pan, add broth and cook until sauce is slightly reduced, chicken is cooked through, and peppers are soft, about 5 to 7 minutes. Stir in oregano, taste, and adjust seasoning, as necessary. Serve immediately over steamed rice or potatoes.