Combine peach preserves, vinegar, horseradish, ginger, salt, and pepper in microwave-safe bowl. Microwave on high until preserves are melted, stirring once halfway through the cooking time, 30 to 60 seconds. Remove and cool to room temperature.
Rinse chicken breasts, pat dry, and place in a resealable plastic bag. Pour cooled marinade over chicken, seal, and refrigerate for 6 to 24 hours, turning chicken occasionally.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Place chicken on preheated grill over indirect heat, cover, and grill until chicken is browned and cooked through, about 30 minutes.