Heat oven to 400 degrees. Cut peaches into 1/2-inch slices. No need to peel.
Toss all ingredients except basil in a 9- by 13-inch baking pan until everything is lightly coated with olive oil. Place pan in oven and bake until meat is cooked through and peaches are softened, about 30 minutes.
Served, topped with the basil. Sauce will be thin, so you can strain the chicken and peaches out, or serve all over pasta, rice or a crusty bread. We like it over a bed of arugula.