Poaching is cooking in simmering water, so a low, slow boil is what you're looking for here. Poaching liquid can be as simple as salt (1 tablespoon kosher per 1/4 pound chicken and 3 to 4 quarts water), plus a few whole peppercorns and a bay leaf. I add root vegetables and herb stems to add more layers to my poached chicken and build a flavor-packed punch to chicken soup or something more complex like pulled chicken curries, pozole or rich, Italian white ragu for sturdy cuts of pasta.
To a large pot, add carrot, celery, garlic, leek, onion, lemon, bay, parsley, thyme, and peppercorns. Set the chicken into pot breast-side up, then add 3 to 4 quarts water to come up sides and just approach covering chicken, then cover and bring to boil. As soon as the pot boils, uncover and add salt, then turn down heat and simmer at low rolling boil, turning the whole chicken twice, every 30 minutes, 1 1/2 hours total. Let the chicken cool 30 minutes more in its own juice.
Remove chicken from cooled broth into shallow dish and remove skin, then pull and remove meat from bones with the assistance of a paring or boning knife. Pull or chop the meat into small or bite-sized pieces.