01Wash rice in 3 or 4 changes of cold water in a large bowl until water is clear, then drain well in a large sieve. Bring 1 3/4 cups water and 1/4 teaspoon salt to a boil, then add rice and cook, covered tightly, over low heat until water is absorbed and rice is tender, about 20 minutes. Remove from heat and let stand, covered and undisturbed, 10 minutes. Fluff rice with a fork and transfer to a bowl to cool to warm.
02Purée all dressing ingredients in a blender until smooth, about 1 minute.
03Toss shredded chicken with lime vinaigrette.
04Put chicken and remaining wrap ingredients in bowls on a large platter with ginger dressing on the side.