Preheat the oven to 375°F (190°C).
In a large oven-safe baking dish, combine the rice, chicken broth, chopped onion, minced garlic, diced carrot, and frozen peas. Stir to mix evenly.
Drizzle 1 tablespoon of olive oil over the rice mixture and sprinkle with dried thyme, salt, and black pepper. Stir gently to distribute the seasonings.
Place the chicken breasts on top of the rice mixture in a single layer.
Brush the chicken breasts with the remaining 1 tablespoon of olive oil and sprinkle paprika evenly over them.
Cover the baking dish tightly with aluminum foil.
Bake in the preheated oven for 40 minutes.
Remove the foil and bake uncovered for an additional 5 minutes, or until the chicken is cooked through and the rice is tender.
Remove from the oven and let rest for 5 minutes before serving.