Place the pieces of chicken, peppers and courgettes into a large bowl (not a metal one). Add the oil, vinegar, Tate & Lyle Dark Soft Brown sugar, mustard and crushed garlic, then season with salt and freshly ground pepper. With a wooden spoon or your hands, mix all the ingredients together thoroughly. Cover with cling film, then refrigerate and leave to marinate for between 1-2 hours.
When ready to cook, soak 8 wooden kebab sticks in hot water for about 5 minutes. Preheat the barbecue or grill.
Thread the chicken and vegetables onto the kebab sticks with the lime wedges. Barbecue or grill for about 12-15 minutes, turning often, until thoroughly cooked.