In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chicken pieces and season with salt and pepper. Cook until browned on all sides, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the diced onion and cook until softened, about 3-4 minutes. Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the rice to the pot and stir to coat it with the oil and onion mixture. Cook for 2 minutes, stirring frequently.
Pour in the chicken broth and add the frozen peas and carrots, thyme, paprika, and bay leaf. Stir to combine.
Return the browned chicken to the pot, bringing the mixture to a boil. Once boiling, reduce the heat to low, cover, and simmer for 20 minutes or until the rice is tender and the liquid is absorbed.
Remove the pot from heat and let it sit, covered, for an additional 5 minutes. Fluff the rice with a fork and remove the bay leaf before serving.
Garnish with fresh parsley and serve warm.