Season the inside of the chicken with a pinch of salt. Place the chicken onto a rotisserie and set the grill on high. Cook for 10 minutes.
Durning that time, quickly mix together the butter, 1 tablespoon of salt, paprika and pepper. Turn the grill down to medium and baste the chicken with the butter mixture. Close the lid and cook for 1 to 1 1/2 hours, basting occasionally, until the internal temperature reaches 180°F when taken in the thigh with a meat thermometer.
Remove from the rotisserie and let stand for 10 to 15 minutes before carving into pieces and serving.