Bring a pot of water to a boil, salt it, add the pasta and cook for 1 minute less than the instructions indicate. Drain and return to the pot.
Meanwhile, place the chicken, large celery pieces, carrot, onion and bay leaf in a pot. Cover with 1 1/2 to 2 quarts water, bring to a boil and let poach for 12 minutes. Remove the chicken, discard the skin and let cool enough to handle. Shred or dice the meat and discard the bones. Strain the poaching liquid into a large measuring cup and add the store-bought chicken stock. (Using the quick-poach liquid alone makes for too thin a flavor, but adding it to store-bought stock works out nicely and stretches a buck.)
Heat the oil in a dutch oven or medium soup pot over medium-high heat. Add the thinly sliced celery, scallions, garlic, chile pepper and the ginger and stir for a couple of minutes. Add the chicken stock mixture and tamari (or soy sauce).
Divide the noodles and shredded chicken among 4 soup bowls. Top with the soup and garnish with the lime wedges and cilantro.