Preheat oven to 400°F. Dress garlic with olive oil, salt and pepper, and wrap tightly in foil. Roast to tender, 40 minutes. Cool and mash cloves into paste.
Place chicken and all poaching ingredients in a pot with enough water to just cover chicken. Bring to a boil then reduce heat to a low simmer. Cook 1 hour, turning chicken once. Cool in poaching liquid then remove skin and bones from chicken. Pull meat into bite-sized pieces and strain stock; reserve.