Southern peaches add a delicious sweetness to just about anything... including barbecue sauce! The key to perfect barbecue chicken is to apply the sauce when the chicken is almost done. This prevents the sauce from burning. — Jennifer Chandler, The Southern Pantry Cookbook.
Boneless, skinless chicken breasts can also be easily grilled indoors on a grill pan.
The barbecue sauce can be made up to 5 days in advance. Store covered in your refrigerator.
Making a homemade barbecue sauce is very easy, but it does take time. You can stir the puréed peaches into your favorite bottled barbecue sauce if you prefer. Just simmer for 5 minutes to meld the flavors.
Put the peaches in a food processor and purée until smooth with some small chunks.
In a large saucepan, combine the ketchup, water, cider vinegar, brown sugar, molasses, red pepper flakes, onion powder, dry mustard, and Worcestershire. Bring the sauce to a boil over high heat. Reduce the heat to medium-low and simmer, stirring occasionally, until the sauce thickens, 20 to 25 minutes.
Stir in the reserved peach purée and cook until the flavors have melded, about 5 more minutes. Measure out 1 cup of sauce. Refrigerate the remaining sauce for another time. (It will keep for up to 5 days in your refrigerator.)
Preheat a clean grill to medium-high with the lid closed for 8 to 10 minutes. Lightly brush the grates with oil.
Generously sprinkle the chicken with the salt and pepper. Place the chicken on the grill. Close the lid and cook, turning once, until no longer pink in the middle, 6 to 8 minutes per side. During the final 5 minutes of cooking, baste the chicken with the barbecue sauce. Remove the chicken from the grill. Serve warm.