Meanwhile, heat oil in a large nonstick skillet over medium-high heat. Add onion and cook, stirring, until soft and beginning to brown, about 3 minutes. Stir in chiles to taste and garlic; cook until the mixture is brown and aromatic, 1 to 2 minutes longer. Add 1 ladleful of the hot broth to the pan, stir, and pour the contents of the pan into the simmering broth. Add chicken, tomatoes and salt to taste. Simmer gently until the chicken is no longer pink inside, about 5 minutes; remove from the heat.