Combine first 7 ingredients in a food processor; process until smooth. Place 6 chicken breast halves and half of herb mixture in a large zip-top plastic bag. Place remaining breast halves and remaining herb mixture in a second large zip-top plastic bag. Seal and marinate in refrigerator 1 hour, turning bags occasionally.
Remove chicken from bag; discard marinade. Let chicken stand 15 minutes. Sprinkle chicken evenly with salt, cumin, and pepper. Place chicken, breast side down, on a grill rack coated with cooking spray. Grill 12 minutes on each side or until a thermometer registers 165°, turning once.