In a large heatproof bowl pour boiling water to cover over the noodles and let them stand for 10 minutes. Drain the noodles and arrange them on a platter or divide them among 6 plates. In a bowl combine the chicken, the carrot and the cucumbers.
Make the dressing: Mince and mash the garlic to a paste with the salt. In a blender blend together the soy sauce, the lime juice, the sugar, the peanut butter, the red pepper flakes and the garlic paste, with the motor running add the oil in a stream, and blend the dressing until it is emulsified.
Pour half the dressing over the chicken mixture, toss the salad well, and arrange it in the center of the noodles. The salad may be made 1 day in advance and kept covered and chilled. Just before serving top the salad with the peanuts. Serve the remaining dressing separately. Serve the salad at room temperature or chilled.