Remove the giblets from the chicken. Discard the liver (it makes the stock bitter) and hold onto everything else. Rinse the chicken with cool water. Put the chicken, vegetables, and giblets in a large stockpot. Pour in enough cold water to cover by 1 inch (about 3 quarts); too much will make the broth taste weak. Toss in the herbs and peppercorns and allow it to slowly come to a boil over medium heat. Skim off the foam then reduce the heat and simmer gently for 1 hour, uncovered, until the chicken is cooked through. As the stock cooks, skim any impurities that rise to the surface; add a little more water if necessary to keep the chicken covered while simmering.
Carefully remove the chicken to a cutting board. When it is cool enough to handle, discard the skin and bones; shred the meat by hand into a storage container and reserve for soups or salads.
In the meantime, set a large fine sieve or a large strainer lined with cheesecloth (the cheesecloth will remove some of the excess fat) over another pot. Pour the stock into the sieve or strainer to strain out the vegetable solids; discard. Use the stock immediately or, if you plan on storing it, place the pot in a sink full of ice water and stir to cool down the stock. Transfer to a storage container, cover, and refrigerate for up to one week, or freeze.
Edited: October 15th, 2009