Making an extra chicken allows you to serve one tonight, and use the other for sandwiches, soups, and salads.
Preheat oven to 450 degrees. On a large rimmed baking sheet, toss the potatoes with 2 tablespoons oil, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper.
To make the seasoning: in a small bowl, combine thyme leaves with 1/4 teaspoon pepper and 2 teaspoons salt; set aside.
Working from neck end of chickens, use your fingers to gently separate skin from flesh, including thigh and leg areas. Distribute thyme mixture under skin of each chicken, dividing evenly; season cavities generously with salt and pepper. Tuck wings under breasts. Using kitchen twine, tie legs together securely on top of chickens. Besides helping them cook evenly and stay moist, this will also help preserve their shape.
Nestle chickens, breast sides up, among potatoes; rub chickens with remaining tablespoon oil, and season each with salt and pepper.
Roast, tossing potatoes occasionally and brushing chicken with pan juices, until an instant-read thermometer inserted in thickest part of thigh (avoiding bone) registers 165 degrees. about 1 hour.
Let chickens rest in a warm spot 10 minutes before serving.
Line a cutting board with wax paper before working with raw poultry. You can toss out the paper when you're done and won't have to disinfect the board.