Place chicken and water in an 8 1/2-quart stove-top pressure cooker and bring to a boil over medium-high. Using a ladle, skim impurities and fat that rise to the top. Add vegetables, bay leaf, and peppercorns.
Lock the lid in place. Over high heat, bring to high pressure. Lower the heat just enough to maintain high pressure and cook for 30 minutes. If time permits, let the pressure decrease naturally, about 20 minutes. Otherwise, quick-release the pressure by setting the cooker under cold running water.
Remove the lid, tilting it away from you to allow any excess steam to escape. Allow stock to cool slightly. Skim off fat if using immediately, or let cool completely (in an ice-water bath, if desired) before transferring to airtight containers. Refrigerate at least 8 hours to allow the fat to accumulate at the top; lift off and discard fat before using or storing stock.
Stock can be refrigerated up to 3 days or frozen up to 3 months; thaw completely in the refrigerator before using.