Prepare the Ingredients: Cube the chicken breast, dice the onions, carrots, and celery, and rinse the rice under cold water until the water runs clear.
Sauté the Vegetables: In a large pan or Dutch oven, heat the olive oil and butter over medium heat. Add the onion and cook for about 3 minutes until soft and translucent. Add the carrots and celery, half the salt, and pepper, stirring well, and cook for another 3 minutes.
Brown the Chicken: Increase the heat to medium-high. Add the chicken cubes to the pan, sprinkling them with the remaining salt, pepper, and paprika. Sauté until the chicken is browned on all sides but not fully cooked, about 5 minutes.
Add Rice and Broth: Stir in the rinsed rice until well combined with the chicken and vegetables. Pour in the chicken broth and add the bay leaf. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 20-25 minutes, or until the rice is tender and the liquid is absorbed.
Rest and Serve: Remove the bay leaf. Let the pilaf rest, covered, for 5 minutes off the heat. Fluff the rice with a fork, garnish with fresh parsley, and serve warm.