Combine first 4 ingredients in a saucepan. Bring to a boil; reduce heat, and simmer 2 to 3 minutes.
Place peaches in a shallow dish. Pour vinegar mixture over peaches, tossing gently to coat. Let stand 10 minutes.
Remove peaches from vinegar mixture, reserving 2 tablespoons mixture. Set aside remaining vinegar mixture.
Whisk together reserved 2 tablespoons vinegar mixture and oil, blending well. Set vinaigrette aside.
Place peach halves, cut sides down, on a lightly greased grill rack. Grill, covered with grill lid, over medium heat (300° to 350°) 5 minutes on each side or until firm and golden, basting with remaining vinegar mixture. Serve peaches with vinaigrette.