Preheat oven to 400ºF.
Slice the top 1/4-inch off the stem end of the garlic head, exposing the cloves. Place the garlic onto a square of aluminum foil and drizzle with about 1 tablespoon EVOO. Wrap the foil up around the garlic to enclose it and roast it in the oven until golden brown and very tender, about 40 minutes.
While the garlic is roasting, place the chicken into a medium pot with the bay leaves and onion. Fill the pot with water and bring up to a simmer. Place the chicken into the pot and simmer until cooked through, about 10 minutes. Remove the cooked chicken from the broth, dice into bite-sized pieces and reserve. Strain the cooking liquid, reserving 4 cups worth.