Cuban chicken and rice (Arroz con Pollo) comes in many variations; however, it always starts with sofrito, a sautéed mixture of onion, bell pepper, and garlic. We use turmeric to color the rice yellow; other versions use annatto seeds or saffron.
Sprinkle chicken with salt, black pepper, and 1 teaspoon oregano. Heat oil in Dutch oven over medium-high heat. Add chicken; cook 8 minutes, browning on all sides. Remove chicken from pan; drizzle with lime juice. Cover; keep warm.
Add onion, bell pepper, and garlic to pan. Cover, reduce heat to low, and cook 10 minutes or until tender. Stir in 1/2 teaspoon oregano, turmeric, and cumin, and cook 1 minute, stirring constantly. Stir in rice and ham; cook 1 minute. Increase heat to medium. Add broth and tomatoes; bring to a boil. Add chicken, nestling into the rice mixture. Cover, reduce heat, and simmer 18 minutes or until liquid is almost absorbed. Stir in peas; cover and cook 3 minutes. Remove from heat; let stand, uncovered, 5 minutes. Sprinkle with olives.