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 1/2 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.