In a large saucepan, combine the whole celery rib, garlic and peppercorns with 6 cups of water. Using a peeler, remove the zest from 2 of the oranges and add the zest to the pot. Season lightly with salt and bring to a boil. Add the chicken and simmer over low heat for 16 minutes. Remove from the heat and let the chicken stand for exactly 30 minutes. Remove the chicken and pull the meat from the bones, discarding the skin. Shred the chicken and let cool. Reserve the broth for another use.
Meanwhile, using a sharp knife, peel the oranges, removing all of the bitter white pith. Working over a strainer set over a large bowl, cut in between the membranes to release the sections. Squeeze the juice from the membranes into the bowl. Whisk in the vinegar and oil and season with salt and pepper.
Add the chicken, sliced celery, orange sections and cheese to the bowl and toss well. Mound the salad on a platter, sprinkle with the almonds and serve.