Heat olive oil in a large skillet over medium heat.
Add the chicken pieces to the skillet and cook for 5-6 minutes, stirring occasionally, until they are browned and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the rinsed rice to the skillet and stir to coat the rice with the oil and aromatics.
Pour in the chicken broth, then add the diced carrots, black pepper, salt, paprika, and dried thyme. Stir well to combine.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 15 minutes.
After 15 minutes, stir in the frozen peas and cooked chicken pieces. Cover again and cook for an additional 5-7 minutes until the rice is tender and the peas are heated through.
Remove from heat and let stand, covered, for 5 minutes.
Fluff the rice with a fork and stir in the chopped fresh parsley before serving.