Combine the chicken breasts and wings, onions, carrots, celery, parsley, garlic, bay leaf, salt and peppercorns in a large stockpot. Add the water and bring to a boil over high heat. Reduce a gentle simmer and cook, uncovered, for 1 1/2 hours, stirring occasionally.
Strain the contents of the pot through a fine-mesh strainer and discard the solids. Transfer the stock to containers; let cool, then refrigerate. Once the stock has chilled, remove the fat that has congealed on the surface. Use immediately or freeze for up to 3 months.