Place all the ingredients in a saucepan set over low heat (about 3 out of 10).
Simmer, uncovered, for 4–5 hours.
Turn off the heat. Remove and discard the herbs.
Transfer the meat to a large bowl and pull it into shreds.
In the pan you’ll see two layers: clear fat on top and dark, intensely flavorful juices underneath. We want to keep both.
Ladle off as much fat as possible into a separate bowl, leaving mostly the cooking juices in the pan.
It’s fine if a bit of fat stays behind—pour everything from the pan into the bowl with the chicken and stir well. Your rillettes are ready!
Potting: Sterilize jam jars or other airtight containers. Layer the mixture and fat—two tablespoons of rillettes followed by one tablespoon of the reserved fat—until the jar is full, finishing with a layer of fat.
Seal tightly and refrigerate for up to 2 weeks, unless you plan to sterilize the jars for longer storage.