Bring a large pot of water to a boil over high heat. Add the chicken, scallions, ginger, and salt and boil for 15 minutes, then turn off the heat, cover the pot and let stand for 15 minutes. If your chicken is larger than 3 pounds, let stand 10 minutes longer.
Just before the chicken is ready, prepare a large ice-water bath. When the chicken is done, remove it from the pot (discarding the cooking liquid) and immediately submerge it in the ice-water bath, which will stop the cooking and give the meat a firmer texture. Let stand 20 minutes, until the chicken is cool enough to handle easily, remove from the water, and pat dry. Pull the chicken meat from the bones, discarding the bones and skin. Shred the meat with your fingers; you should have about 4 cups. (This step can be done a day ahead.)
In a large saucepan, bring the stock to a boil over high heat. Taste for seasoning and add fish sauce, if needed.
To ready the garnishes, arrange the basil, bean sprouts, lime wedges, and chiles on a platter and place on the table.