Set the chicken in a slow cooker and arrange the onions, carrot and celery around it. Add the water, parsley, thyme, bay leaf and peppercorns. Cook on high power until the broth is very flavorful, about 6 hours.
Gently remove the chicken from the slow cooker and reserve for later use. Strain the broth into a large bowl and skim the fat from the surface. Season generously with salt. Let cool, then cover and refrigerate.
The broth can be refrigerated for up to 3 days or frozen for up to 1 month. The reserved chicken can be refrigerated for 3 days; it can be shredded and used in chicken noodle soup, chicken salad or barbecued pulled-chicken sandwiches.