Cut chicken breasts in half. Place chicken in a plastic bag set in a large bowl. For marinade, drain pineapple, reserving 1/4 cup juice. In a bowl combine pineapple, reserved juice, lemon slices, ketchup, honey, Worcestershire sauce, garlic, salt, and rosemary. Pour marinade over chicken; seal bag. Marinate in the refrigerator for at least 2 hours or up to 24 hours, turning bag occasionally.
Prepare grill for indirect grilling. Test for medium heat above the drip pan. Drain chicken, reserving marinade. Place chicken, bone side down, on the grill rack over the drip pan. Cover and grill for 50 to 60 minutes or until an instant-read thermometer inserted into the thickest portion of one piece registers 170 degrees F and no pink remains, turning and brushing with about 1/4 cup of the reserved marinade halfway through grilling.
For sauce, in a medium saucepan combine remaining reserved marinade and cornstarch. Cook and stir over medium heat until thickened and bubbly. Cook and stir 2 minutes more. To serve, spoon sauce over chicken and rice. Makes 4 servings.