To prepare sauce, drain yogurt in a strainer lined with cheesecloth 2 hours or overnight. Transfer to a bowl and stir in garlic, olive oil, dill, lemon juice and salt.
To prepare chicken, preheat oven to 450F. Coat a large wire rack with cooking spray and place on a rimmed baking sheet.
Combine basil, mint, dill, oil, garlic, and lemon rind and juice in a large bowl. Add chicken; toss well to coat. Arrange chicken in a single layer on wire rack; sprinkle with salt and pepper.
Roast chicken breasts 30 to 40 minutes or until an instant-read thermometer inserted into the thickest part of the breast registers 170F. Roast thighs 35 to 45 minutes or until an instant-read thermometer inserted into the thickest part of the thigh registers 180F. Serve immediately or room temperature, with lemon wedges and Yogurt Dill Sauce.