Place first 10 ingredients in a blender; process until smooth.
Pour into a large zip-top plastic bag.
Add chicken; turn to coat.
Marinate chicken in refrigerator at least 4 hours or overnight.
Combine 3/4 cup yogurt and next 4 ingredients (through 1/4 teaspoon salt) in a small bowl.
Cover and refrigerate.
Remove chicken from refrigerator, and let stand at room temperature 45 minutes.
Prepare grill for indirect grilling. If using a gas grill, heat one side to medium-high and leave one side with no heat. If using a charcoal grill, arrange hot coals on either side of charcoal grate, leaving an empty space in the middle.
Remove chicken from marinade, and discard remaining marinade.
Place chicken on unheated part of grill rack coated with cooking spray.
Close lid and grill 90 minutes or until a thermometer inserted into meaty part of thigh registers 165°F, turning chicken every 20 minutes.
Serve 1 chicken quarter each with about 1/3 cup of raita.