Combine Spicy Peach Glaze ingredients in a medium bowl and season with salt and pepper to taste. I like to use an emulsion blender to make the glaze smooth. Reserve 1/2 cup.
Preheat grill. Brush the chicken with olive oil and season with salt and pepper to taste. Place skin-side down and cook for 6 to 7 minutes, until golden brown. Turn over and continue cooking for 5 to 6 minutes. Brush both sides with the peach glaze and continue cooking an additional 4 to 5 minutes.
Place peach halves, cut side down on the grill and grill for 2 minutes. Turn over and brush with the reserved 1/2 cup of peach glaze, grill for 3 to 4 more minutes until peaches are soft.