Prepare an ice bath. Bring a medium saucepan of water to a boil. Score an X in the bottom of the peaches; place in boiling water 30 seconds. Using a slotted spoon, transfer peaches to ice bath; let cool completely. Drain; peel peaches, starting at the X. Cut into quarters, and remove pits.
Roast 1 pepper over a gas flame or under the broiler, turning often, until it is charred on all sides. Transfer to a bowl, and cover with plastic wrap. Let cool at least 10 minutes. Using a paper towel, rub off charred skin, and discard. Remove seeds and ribs, and discard.
Make peach-pepper sauce: Place 1 roasted pepper and four peach quarters in the jar of a blender, and puree until mixture is smooth. Season with salt and pepper.
Heat a grill or a grill pan over medium heat. Place chicken in a medium bowl, and coat with 1/2 cup peach-pepper sauce and the oil. Let marinate 30 minutes in the refrigerator. Cut remaining pepper into 1-inch pieces. Cut remaining peach wedges into 1-inch chunks. Skewer chicken, alternating it with peaches and peppers. Grill kabobs, rotating as needed, until chicken is cooked through and peaches and peppers are nicely browned, 10 to 15 minutes. Serve immediately with remaining peach-pepper sauce.