Combine first 10 ingredients in a food processor; process until smooth. Combine preserves mixture and chicken in a zip-top plastic bag. Seal and marinate in refrigerator 2 hours, turning the bag occasionally.
Remove chicken from bag; reserve marinade. Sprinkle chicken evenly with salt; place chicken on grill rack coated with cooking spray. Grill 6 minutes on each side or until chicken is done.
Combine the reserved sauce and 1 cup water in a medium saucepan over medium-high heat; bring to a boil. Reduce heat, and simmer until reduced to 3/4 cup (about 8 minutes). Serve sauce over chicken and rice.