Unlike pasta that is being served warm, noodles used in cold dishes are drained, rinsed with cool water, and drained again until dry. Tossing the ingredients together at just the last moment keeps colors bright and flavors distinct.
In a small bowl, stir together ingredients for dressing until sugar is dissolved. Set aside.
In a large pot of salted boiling water, cook soba noodles according to package instructions. Drain, rinse with cool running water, and drain again until dry.
Place noodles in a large bowl and toss with dressing. Let sit 5 minutes. Toss in carrots and chicken. Sprinkle with scallions. Serves 4 to