Step 1: Make the wet rub: Place the garlic and salt in a mortar, and using a pestle, pound until a paste forms. (Or use a small food processor or a glass bowl and wooden spoon.) Work in the paprika, cumin, pepper, ají amarillo paste, huacatay paste, lime juice (save the rinds), and olive oil.
Step 2: Place the spatchcocked chicken in a nonreactive baking dish with the lime halves and coat it on all sides with the wet rub. Cover and refrigerate for at least 6 hours, preferably overnight.
Step 3: Set up the grill for direct grilling and preheat the grill to medium. When ready to cook, brush and oil the grill grate. Scrape any excess rub off the chicken and discard the rub. Place the chicken (flat) in the center of the grate, skin side up.
Step 4: Grill the bird for about 20 minutes, then turn with tongs. Grill until the skin is golden brown and crisp and the meat is cooked through, about 40 minutes in all. Use an instant-read meat thermometer to test for doneness; the internal temperature in the thickest part of the thigh should be 165 degrees F. Transfer the chicken to a platter. Let the bird rest for a few minutes, then serve with the Aji Amarillo Sauce.
Note: If you can’t find aji Amarillo, substitute 1 grilled, peeled, cored, seeded, and diced yellow bell pepper, plus ½ to 1 teaspoon cayenne pepper.
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