In a large pot or Dutch oven, heat the vegetable oil over medium heat. Add the chicken pieces and cook until browned on all sides. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion, red bell pepper, and green bell pepper. Cook until the vegetables are softened, about 5 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the ground cumin, ground paprika, ground turmeric, dried oregano, salt, and black pepper to the pot. Stir to combine.
Mix in the tomato sauce and cook for 2-3 minutes to let the flavors meld.
Return the browned chicken pieces to the pot.
Pour in the chicken broth and bring to a boil.
Stir in the rinsed rice, making sure it's evenly distributed.
Reduce the heat to low, cover the pot, and simmer for 20-25 minutes, or until the rice is cooked and the chicken is tender.
In the last 10 minutes of cooking, add the frozen peas and diced carrots.
Once the rice and chicken are fully cooked, remove the pot from heat.
Stir in the chopped fresh cilantro, sliced green olives, and capers (if using).
Drizzle with lime juice before serving.
Enjoy your meal!