Preheat barbecue for high heat, and lightly oil cooking grate.
Rub chicken breast fillet with salt and pepper. Cook on hot barbecue for 10 to 15 minutes on each side, until no longer pink and juices run clear. Remove from heat, set aside, and keep warm.
Heat oil in a medium frying pan over medium heat, and sauté garlic for about 1 minute. Mix in ginger and mangoes, and cook 3 to 4 minutes, until mangoes are tender. Pour in the cider vinegar and white wine. Season with salt and pepper. Stir in coriander, and remove from heat. Spoon over the barbecued chicken to serve.