Preheat oven to 350 degrees.

Melt the butter in a large heavy skillet over med-high heat and cook chicken for about 4 minutes on each side, or until browned.

Transfer the chicken to a pie plate or bowl.

Decrease heat to medium and sauté onion, celery, and carrots until the onion is soft and translucent, about 5 minutes.

Add the rice and stir to coat in the butter.

Add the chicken broth; return the chicken and any juices to the pan.

Add the salt and pepper.

Let the chicken come to a boil over med-high heat; cover with an oven-proof lid or foil and cook in the oven for 30 minutes, or until the chicken is cooked through and the rice is tender and the liquid is absorbed.