In a large nonstick Dutch oven or saucepan, heat the oil. Saute the bell peppers and onion until softened, about 5 minutes. Add the chicken; cook, breaking apart with a wooden spoon, until no longer pink, 5-7 minutes.
Sprinkle with the flour, chili powder, cumin, cocoa powder, and cayenne; cook, stirring briskly and constantly, 1 minute. Stir in the tomatoes and vinegar; bring to a boil. Reduce the heat and simmer, stirring frequently, until thick, 30-40 minutes. Stir in the chickpeas; simmer until heated through, about 5 minutes.