Fill a small sauce pan half full with water, add 1 tsp salt and bring to boil. Add chicken breasts. Bring the water back to boil, remove the pan from the heat and cover tightly. Let stand for 20 minutes. The chicken should be firm yet still yield a bit to the touch. Remove the chicken from the pan and discard the water. When cool enough to handle, shred with your fingers into thin pieces, pulling the meat along its natural grain. Put the chicken in a large bowl and let it cool to room temperature.
Meanwhile, put the onion in a small bowl and add the vinegar just to cover. set aside for 15 minutes; the vinegar will reduce the harshness of the onion. Drain well and add to the bowl with the chicken, along with the cabbage, carrot and cilantro.
To make the dressing, using a mortar and pestle (I used a blender), mash the chiles, garlic, sugar and salt together. scrape the paste into a bowl and add the fish sauce and rice vinegar, stirring to dissolve the sugar and salt and to combine well.
Just before serving, pour the dressing over the salad and toss to mix well. Taste and adjust the flavors to your liking (I don’t think it needs anything else, the flavors are perfectly balanced). Serve.