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Stir together 1 cup yogurt, 2 tablespoons oil, 1 tablespoon lemon juice, salt and spices.
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Add chicken and turn until well coated.
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Marinate at room temperature for 20 minutes.
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While the chicken is marinating, preheat grill.
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While grill is heating, stir together remaining 1 1/4 cups yogurt and 1 1/2 tablespoons lemon juice and salt to taste.
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Reduce grill to moderate heat.
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Grill chicken (discard marinade), on lightly oiled grill rack, turning occasionally (closing grill between turns), until cooked through, 10 to 12 minutes total.
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Transfer chicken to a platter.
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Toss together mint, shallot and remaining oil in a small bowl.
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Drizzle chicken with yogurt sauce and top with mint salad.