Using the flat side of a chefs knife, mash the garlic and 1 1/2 teaspoons salt into a paste. Transfer to a bowl, then stir in the ancho chile powder, chipotle chile and adobo sauce, paprika and lime juice.
Using your fingers, loosen the chicken skin all over, being careful not to tear the skin and avoiding the area closest to the removed backbone. Rub the paste all over the chicken, smearing it first under the skin, then on the underside of the chicken, then over the skin. Transfer to a gallon-size resealable plastic bag and refrigerate for at least 4 hours or overnight.
Preheat a grill to medium. Position the chicken, skin side down, on an oiled cooking grate, using tongs and a spatula to lay the chicken flat and stretch it out to its full size. Grill, turning every 10 minutes, until an instant-read thermometer registers 170 degrees or juices run clear when pierced with a knife and the skin is crisp, 35 to 40 minutes. (If any flare-ups occur, move the chicken to a different spot on the grill and cover briefly.) Let rest for 10 minutes before carving.