Heat oven to 400° F. Rinse the chicken and pat it dry with paper towels. Place in a roasting pan. Combine 2 tablespoons of the oil, 1 1/2 teaspoons of the salt, 1/2 teaspoon of the pepper, and the curry powder. Drizzle the chicken with the mixture and rub to coat. Toss the carrots with the remaining salt, pepper, and oil and place in the pan. Roast, stirring once, until the chicken is cooked through and a thigh registers 180° F on a meat thermometer, about 45 minutes. Serve with cooked rice.