Soak skewers in water at least 30 minutes to prevent burning. Meanwhile, cut each chicken breast in half lengthwise, then cut crosswise to make 10 (about 1-inch) pieces. Cut onions into 2-inch pieces (30 pieces total). Cut bacon slices in half crosswise.
Heat gas or charcoal grill. Push 1 skewer through end of 1 bacon piece, then through middle of 1 chicken piece and back through other end of bacon piece; add 2 onion pieces, then repeat with another bacon piece and chicken piece. Place on large plate or tray. Repeat to make remaining kabobs.
Place kabobs on grill over medium heat. Cover grill; cook 5 minutes. Turn kabobs; brush with half of the barbecue sauce. Cover; cook 5 minutes. Turn kabobs; brush with remaining sauce. Cover; cook about 1 minute longer or until chicken is no longer pink in center. If desired, serve with additional barbecue sauce for dipping.