Heat 2 tablespoons olive oil in a large skillet over medium heat. Season the chicken with the rosemary on both sides; cook the chicken in the hot oil until browned evenly, 3 to 4 minutes per side. Remove the chicken from the pan and set aside.
Pour 1 tablespoon olive oil into the skillet. Cook and stir the garlic in the hot oil until fragrant, about 1 minute. Add the tomato sauce, Italian seasoning, cayenne pepper, sugar, bay leaf, and red pepper flakes to the skillet; stir. Return the chicken to the skillet; cover and reduce heat to medium-low. Simmer until the chicken is no longer pink in the center and the juices run clear, 10 to 12 minutes.
Stir the garbanzo beans into the skillet; continue cooking until the beans are heated, 2 to 3 minutes more.
