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Prepare a medium-high (400°F) gas or charcoal grill fire.
In a large bowl, stir the vinegar, sugar, chiles, and 1-1/2 tsp. salt until the sugar dissolves. Reserve 2 Tbs. dressing in a small bowl. Add the carrots and fennel to the large bowl and toss; set aside.
Pat the chicken dry and generously season with salt and pepper. Oil the grill grate. Grill the chicken, turning once, until cooked through, about 10 minutes. Transfer to a cutting board, and let rest for a couple of minutes.
Meanwhile, prepare the noodles according to package directions. Drain, rinse briefly under cold running water, and transfer to the large bowl. Add the cabbage and sesame oil, toss well, and season to taste with salt, pepper, and more sesame oil. Transfer the salad to a serving platter or plates. Slice the chicken thinly and arrange on top. Drizzle with the reserved dressing, garnish with fennel fronds, and serve.
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