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Remove the chicken from the marinade and discard the marinade. Place the chicken on the grill and cook until golden and slightly charred, about 3 minutes per side. Place the lemon halves cut-side down on the grill grate and grill until charred, about 4 minutes.
Add the arugula to a platter and drizzle very lightly with olive oil. Remove the chicken from the grill and shingle across the bed of arugula. Squeeze some lemon juice over the chicken and serve.