Melt the butter in a large skillet with a lid over medium heat, and sear the chicken breasts, skin side down, for 5 minutes, until the chicken starts to brown.
Turn the chicken breasts over, add the potatoes and carrots, and sprinkle with paprika, garlic powder, salt, and pepper. Cover and cook over medium heat for 35 to 45 minutes, stirring occasionally, until the potatoes are tender, the chicken is no longer pink inside, and the chicken and vegetables have brown, crisp spots on the bottom.