Season chicken with 1/2 teaspoon salt and 1/8 teaspoon pepper. Coat with flour. In heavy pot, heat 1 tablespoon oil over medium-high heat. Brown chicken in batches, about 3 minutes per side. Add additional tablespoon oil as needed. Remove from pot.
Reduce heat to medium. Add onion; cook, stirring occasionally, until softened, 5 minutes. Add garlic; cook 1 minute. Stir in rice to coat with oil.
Add chicken, broth, remaining salt and pepper, the oregano and Sazon seasoning; simmer, covered, 20 minutes.
Stir in pigeon peas and pimiento; simmer 10 minutes.
Serve directly from pot, if desired. Garnish with parsley.
