Cut open the chitterlings, scrape off and discard the fat. Wash thoroughly, until the water runs clear.
Place in a pot and cover with water. Add garlic, salt and cayenne pepper. Bring to a boil, then turn down the heat and simmer for about 2 hours, until tender.
Beat together the egg and water. Place breadcrumbs in a shallow dish.
Drain chitterlings and cut into two-inch pieces. Dip each piece into egg and water mixture, then into the breadcrumbs.
Fry in hot, 375°F oil, until brown. Drain on paper towels.