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1
Whisk together lime juice, honey, red pepper flakes, and 3/4 teaspoon salt in a large bowl and add oil in a slow stream, whisking.
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2
Transfer chicken to a 1-gallon sealable plastic bag and add 1/3 cup lime vinaigrette, then seal bag. Marinate chicken at room temperature 15 minutes.
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3
Transfer another 1/3 cup lime vinaigrette to a bowl, stir in tomatoes and shallots, and marinate until chicken is finished cooking. Transfer another 1/3 cup lime vinaigrette to a large bowl and set aside for cooked chicken. Put remaining lime vinaigrette in a small airtight container and reserve for lettuce wraps (recipe follows).
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4
Remove chicken from bag, discarding marinade, and sprinkle all over with remaining 1 1/2 teaspoons salt.
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5
Open vents on bottom of grill and on lid. Light a large chimney starter of charcoal briquettes (80 to 100) and pour them evenly over 1 side of bottom rack (you will have a double or triple layer of briquettes).
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6
When charcoal turns grayish white (after 15 to 20 minutes) and you can hold your hand 5 inches above rack for 3 to 4 seconds, sear chicken breasts, starting with skin sides down, on a lightly oiled rack over coals, uncovered, turning once, until well browned, 5 to 6 minutes total.
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7
Move browned chicken breasts to side of grill with no coals and cook, covered with lid, turning over occasionally, until just cooked through, 12 to 15 minutes more.
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8
Preheat all burners on high, covered, 10 minutes, then adjust heat to moderately high.
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9
Sear chicken on lightly oiled grill rack, covered with lid, turning frequently, until well browned, about 6 minutes total.
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10
Turn off 1 burner (middle burner if there are 3) and arrange all seared chicken on rack above shut-off burner. Cook seared chicken, covered with lid, turning over once, until just cooked through, 10 to 15 minutes.
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11
Transfer hot grilled chicken to large bowl with lime vinaigrette and turn to coat. Leave in bowl 5 minutes, then transfer to a platter and loosely cover with foil.
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12
Toss together mesclun, basil, tomato mixture, and salt to taste. Drizzle some lime vinaigrette from bowl over chicken and serve with mesclun salad.
