Heat the olive oil in a large pot or Dutch oven over medium-high heat.
Season the chicken pieces with salt, black pepper, and paprika. Add them to the pot and brown on all sides, about 5 minutes. Remove the chicken and set aside.
In the same pot, add the diced onion and bell pepper. Sauté until softened, about 3-4 minutes. Add the minced garlic and sauté for an additional 1-2 minutes until fragrant.
Stir in the rice, ensuring it is well coated with the oil and mixed with the vegetables.
Pour in the chicken broth and add the dried oregano. Bring the mixture to a boil.
Once boiling, return the browned chicken to the pot, reduce the heat to low, and cover with a lid. Simmer for about 20 minutes or until the rice is cooked and has absorbed most of the liquid.
In the last 5 minutes of cooking, add the frozen peas and carrots if using. Stir gently to combine, then cover until fully heated through.
Remove from heat and let rest for a few minutes before serving. Garnish with chopped parsley if desired.