In a small bowl, whisk together the lime juice, sugar, fish sauce, and chile paste. Set aside.
Heat the oil in a large skillet over medium heat. Add the ginger and garlic and stir-fry, until fragrant, about 2 minutes. Add the chicken and salt, and stir-fry the meat, breaking it up with a wooden spoon, until just cooked through, about 6 minutes. Stir in the scallions, carrot, and water chestnuts. Transfer the chicken mixture to a bowl and cool. Stir in the lime juice mixture, mint, and coriander. Refrigerate until ready to serve.
Arrange the lettuce leaves on a platter and fill each with some of the chicken salad. Serve with lime wedges.
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