In a saucepot, add all of the ingredients except the chicken. Cook over medium heat for 20 minutes, or until the peaches have become tender.
Carefully pour contents into a blender or food processor and pulse until smooth. Add back to saucepot and set aside
Preheat the oven to 375°
Lay chicken legs and thighs on a baking rack set over a baking sheet. Pat dry and season with salt and pepper. Use a basting brush to brush barbeque sauce liberally over each piece of chicken.
Bake for 40-45 minutes, or until the chicken reaches 165°, basting every 15 minutes.
During the last 5 minutes, turn the broil on high to allow the sauce to caramelize. Remove from oven and rest for 5 minutes before serving.