Cut chicken into large 1-inch chunks. Place into medium bowl and add ¼ cup of BBQ sauce, salt, and pepper. Toss together until evenly coated. Cover and refrigerate for 1 hour. In the meantime, soak wooden skewers in water.
When chicken is done marinating, prepare the other skewer ingredients. Slice the top, bottom, and skin off the pineapple. Cut into chunks, making sure to remove the tough core pieces. Cut the red onion into large pieces. Fold each slice of ham 3 times to make a wedge.
Preheat grill to medium-high. Assemble the skewers by organizing the ingredients in a pattern such as this: pineapple chunk, ham wedge, two pieces of onion, and marinated chicken. Repeat this pattern again on the skewers and then on the remaining wooden skewers.
Grease the grill with non-stick spray or canola oil. Place chicken skewers on grill over the flame. Rotate after 6 minutes and cook for 4 more minutes. Remove from the grill and brush skewers with the remaining BBQ sauce. Serve immediately.