Place dressing ingredients in a small screw top jar, season with salt and shake well before using.
Cook rice noodles according to the packet instructions until al dente (6-8 minutes). Drain and refresh under cold water, drain well. Place in a large bowl.
Thinly slice the carrots lengthwise (a vegetable peeler is good for this), and add to the noodles. Add the radishes and basil with the sliced chicken. Drizzle over the dressing and toss gently to combine.
To cook the chicken:Cut through each chicken breast horizontally and open out (as if you were reading a book). Cover the opened-out chicken with baking paper and using a meat mallet or base of a small heavy saucepan, pound the chicken until it's about 5mm thick. Rub in a little oil and barbecue, grill or pan-fry for 2 minutes on each side or until the chicken meat is no longer springy.