Put chicken in a large pot and pour in 4 qts. cold water. Heat over medium heat, uncovered and skimming off any foam that forms on the surface, until simmering, about 40 minutes. Cover and simmer, skimming every 30 minutes, until liquid is reduced to about 2 qts., 3 to 4 hours.
With scissors, cut small slits in kombu to help release flavor. Add to pot and simmer, covered, until kombu begins to fall apart, 45 minutes to 1 1/2 hours.
Strain broth through a fine-mesh strainer into a storage container and discard solids. Let broth cool to room temperature, then chill until cold. Skim off fat before using.
*Find kombu at Asian markets and some well-stocked grocery stores.
Make ahead: Up to 4 days, chilled, or up to 3 months frozen.