Special equipment: 12 wooden skewers for skewering the chicken and vegetables
To make the marinade: In a saucepan whisk together the soy sauce, Sherry, sugar, ginger, and garlic and season with salt and pepper. Bring the mixture to a boil, lower the heat, and simmer for 5 minutes. Let the marinade cool. (The marinade can be made in advance, and refrigerated for up to 2 weeks.)
To make the skewers: On each skewer alternate 3 pieces of chicken with 2 scallion lengths and 2 water chestnuts. (Skewer the water chestnuts carefully so they don't split; and begin and end with the chicken.) Arrange the skewers in a large shallow baking dish and pour the marinade over the chicken and vegetables. Marinate at room temperature, turning once, for 30 minutes. (The skewers can be marinated up to overnight.)
Arrange an oven rack about 4 inches from the broiler and preheat.
Arrange the skewers on a foil-lined baking sheet, reserving the marinade. Broil the skewers, basting occasionally for the first 6 minutes. Continue broil, turning occasionally, until the chicken is just cooked through, about 10 minutes. Discard any remaining marinade. Transfer the skewers to a platter and serve with the lemon wedges and mustard.