Step 1: Heat grill to medium (350° to 450°).
Step 2: Mix soy sauce, oil, five-spice powder, and sugar in a shallow dish. Turn chicken in marinade and let stand 5 to 10 minutes.
Step 3: Heat a large pot of water to boiling.
Step 4: Drain chicken, discarding marinade. Oil cooking grate, using tongs and a wad of oiled paper towels.
Step 5: Grill chicken, covered, turning once, until cooked through, 10 to 12 minutes. Transfer to a cutting board and let rest 5 minutes.
Step 6: Add vermicelli to pot of water and turn off heat. Let stand until soft, 5 to 10 minutes; drain.
Step 7: Divide noodles among dinner bowls. Thickly slice chicken, set on noodles, and top with carrots, herbs, and peanuts.
Step 8: Serve with dressing.
Step 9: Chile Lime Dressing:
Mix 1/2 cup hot water and the sugar in a small bowl until sugar dissolves.
Step 10: Stir in remaining ingredients.