1. Place chicken in a large bowl. Add barbecue sauce; toss. Cover, and refrigerate for at least 30 minutes or overnight.

2. Place the water in a large saucepan. Add 1 tablespoon salt and potatoes. Bring to a boil over high heat. Reduce heat; simmer until potatoes are almost tender when pierced with a knife, about 10 minutes. Do not overcook. Drain; halve. Set aside.

3. Thread 4 cubes of chicken, alternating with potatoes and squash, on each of 8 skewers. Gently brush vegetables with a little olive oil. Season with remaining 1/2 tablespoon salt and the pepper.

4. Arrange skewers, off direct heat, on a medium-hot grill. Grill, rotating skewers and brushing with olive oil as necessary to prevent sticking, until cooked through, about 12 minutes depending on heat of grill. Vegetables should be soft and slightly charred. Serve with choice of condiments.