Spatchcock the chicken by cutting out the backbone with kitchen shears. Season all over with salt, and let rest at room temperature for 30 minutes while you heat up the grill.
Over a wood or charcoal fire, grill the chicken skin-side up over direct heat for about 15 minutes, then flip it and grill skin-side down another 10. (Make sure you move your chicken around because the fat will start rendering, which can affect the flames.) Remove it from the grill and let it rest 6–7 minutes, then return it to the grill, skin-side down, over indirect heat and let it cook until the skin is crispy.
Serve whole chicken breasts, thighs, wings, and drumsticks with potatoes, frijoles de la olla, salsas, and warm tortillas.