There are few delights like a great rotisserie chicken—that thin skin that has browned and crisped in the bird's own slowly rendering fat is something to live life for.
Pat chicken dry with paper towels. Sprinkle with salt all over outside and in cavity. Set chicken on a wire rack set in a baking sheet and place in refrigerator overnight.
Using a skewer, poke holes all over chicken. Tuck wings underneath chicken and truss legs together with butcher twine. Run spit through cavity of chicken and secure with rotisserie forks.
Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and arrange the coals on either side of the charcoal grate. Place a foil pan between two piles of coals. Add an additional 1/4-1/3 chimney of charcoal on each pile of coals; let sit until all charcoal is lit and covered in gray ash.. Place spit on rotisserie and brush chicken all over with butter. Cover grill and cook at medium high heat until skin has browned and chicken registers between 155 and 160oF on an instant read thermometer inserted into the thickest part of breast, 30 to 45 minutes. Remove from grill and let rest for 10 minutes. Remove spit, carve, and serve.