Place rice in a saucepan with 4 cups of water. Bring to a boil, then reduce heat to low, cover and simmer for 20 minutes or until rice is tender. Prepare chicken while the rice is cooking.
In a medium bowl, stir together the flour, 1/2 teaspoon salt, pepper, paprika, and thyme. Use a finger to grind the thyme to a powder in the palm of your hand before adding. Pound out the chicken breasts to 1/4 inch. Coat the chicken breasts in the flour mixture. Reserve 2 tablespoons of the flour mixture for the gravy.
Melt butter in a large skillet over medium heat. Place chicken in the skillet, and cook for about 2 minutes on each side, until the chicken is golden brown, and the juices run clear. Remove chicken from the pan, leaving the drippings and crusty bits in.
Whisk together 3/4 cup stock, 2 tablespoons of the flour mixture, and 1/4 teaspoon salt. Whisk into the skillet, scraping the browned bits from the bottom of the pan. Cook over medium heat, stirring constantly, until thick and bubbly. Add additional stock 1 tablespoon at a time if the gravy is too thick. Serve chicken alongside rice topped with gravy.