In a food processor, combine all of the ingredients except the chicken and lemon wedges and process to a paste. Spread the paste all over the chicken and refrigerate for at least 1 hour or up to 4 hours.
Light a charcoal grill. When the coals are hot, move them to one side of the grill to create a high-heat zone. Oil the grate and place the chicken on it, skin side up, opposite the coals. Cover and grill the chicken until browned and just cooked through, about 30 minutes. Turn the breasts over and grill over high heat until the skin is crisp and lightly charred, about 2 minutes longer. Let the breasts rest for 5 minutes, then serve with lemon wedges.