Trim fat from pork. Combine bourbon, mustard, and thyme in a large heavy-duty, zip-top plastic bag. Add tenderloin; marinate in refrigerator 8 hours.
Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Remove tenderloin from bag, reserving marinade. Place tenderloin on rack. Grill, covered, 9 minutes; turn tenderloin, and brush with marinade. Cover and grill 7 to 9 additional minutes or until meat thermometer inserted into thickest part of tenderloin registers 160°.
Combine peaches, chutney, and green onion in a medium bowl, stirring well. Cut pork into thin slices, and spoon peach chutney over slices.