Preheat an outdoor grill for high heat and lightly oil the grate.

Thread chicken, green bell pepper, onion, and red bell pepper pieces onto skewers alternately.

Cook skewers on the preheated grill, turning and brushing frequently with barbeque sauce, until chicken is no longer pink in the center and the juices run clear, about 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).