Into a heavy saucepan over medium heat, put the chicken, thyme, ¼ teaspoon of butter, salt, and pepper. Add cold water to cover, bring the liquid to a boil, reduce the heat, cover, and simmer for 1 hour, or until the chicken is done. Remove the chicken from the broth to cool. Strain and reserve the broth. When the chicken can be handled, separate the meat from the skin and bones and discard them. Cut the chicken into pieces and set aside.

Preheat the oven to 500°F. Put the corn, onion, tomatoes, lima beans, okra, bacon, and reserved broth into a large, heavy stockpot over medium heat. Add water, if necessary, to cover. Bring the liquid to a boil, lower the heat, and simmer gently until the vegetables are just barely cooked. Remove the pot from the heat, strain, and reserve the broth. In a small saucepan over low heat, melt the remaining 2 tablespoons of butter. Add the flour and whisk to blend. Add 2 cups of the broth and whisk until well blended and the liquid thickens. In a large bowl, mix the chicken, vegetables, and sauce together. Pour the ingredients into the piecrust, then add the piecrust top. Pierce the top crust with a fork several times. Bake for 15 minutes, then lower the heat to 375°F and bake for 20 minutes, or until golden.