Prepare the grill. Then lightly spray the grill rack with cooking spray.
Lightly crush cherries in a small saucepan.
Add the wine or water and next 6 ingredients (through preserves). Bring the mixture to a boil; reduce heat, and simmer, stirring occasionally, 10 minutes.
Grill the chicken, covered, for 4 minutes on each side or until it is cooked through.