In a small saucepan, mix the vinegar with the sugar and cook over moderate heat, stirring, until the sugar dissolves. Add 1 teaspoon of the garlic and the crushed red pepper and let cool.
In a large bowl, mix 2 tablespoons of the sweet seasoned vinegar with the remaining 3 teaspoons of garlic and the soy sauce, ginger and sesame oil. Set aside 2 tablespoons of this soy marinade. Add the chicken to the remaining marinade in the bowl and refrigerate for at least 1 hour or overnight.
Light a grill or preheat the broiler and position a rack 6 inches from the heat. Remove the chicken from the marinade and let it drain, then grill or broil for about 2 minutes per side, until browned and cooked through. Transfer the chicken to a cutting board and let rest for 5 minutes. Cut the chicken crosswise into 1/2-inch strips and mound in a bowl.
In a medium bowl, toss the cucumber with the remaining sweet seasoned vinegar. Put the bean sprouts, mint, cilantro and peanuts in separate bowls. Arrange the lettuce leaves in a basket. Add the water to the reserved 2 tablespoons of soy marinade. Let guests wrap the chicken and garnishes in lettuce leaves and pass the soy marinade and cucumber salad separately.
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