In a glass baking dish or large freezer bag, combine all the marinade ingredients. Add the chicken, eggplant and bell peppers. Coat well. Cover the dish or seal the bag. Refrigerate for 6 hours or overnight.
In a bowl, combine all the ingredients. Season with salt and pepper. Refrigerate.
Preheat the grill, setting the burners to medium.
Thread 5 eggplant cubes on each skewer, alternating with 4 chicken cubes and 3 bell pepper squares. Season with salt and pepper.
Oil the grate. Grill the brochettes until the chicken is cooked through, 4 to 5 minutes per side.