To make the marinade, combine the minced garlic, lemon juice, rigani and sugar in a bowl. Whisk together the ingredients while slowly pouring the olive oil in a thin stream into the bowl. Season to taste with salt and pepper.
In a separate bowl, combine the chicken cubes and enough of the marinade to completely coat the chicken. Cover and refrigerate for at least six hours. Reserve the remaining marinade to baste the vegetables and chicken on the grill.
Prepare the barbecue grill.
Soak long wooden skewers in water for about 20 minutes. Remove the chicken from the refrigerator and allow it to return to room temperature. Alternately thread the chicken cubes, peppers, onions and tomatoes on the skewers. Brush the grill rack with olive oil before placing the kebabs on the grill. Cook the kebabs basting and turning frequently until done. Serve immediately.