Place all the ingredients in a large soup pot and bring to a boil over medium-high heat. Reduce the heat to a simmer for 3 to 4 hours, occasionally skimming off any foam that comes to the surface.
Remove the chicken pieces to use for another recipe and vegetables.
Strain the broth through a fine-mesh strainer. Transfer the broth into jars and refrigerate for 1 week or store in heavy-duty zip bags and freeze for 2 to 3 months.