1. Heat the oven to 375°. Coat the chicken with 3 teaspoons of the oil. Put the pieces, skin-side up, in a large roasting pan. Sprinkle the chicken with the oregano, 1 tablespoon of the vermouth, the lemon juice, salt, and pepper. Drizzle the remaining teaspoon oil over the top.
2. Cook the chicken until the breasts are just done, about 25 minutes. Remove the breasts and wings and continue to cook the drumsticks and thighs until done, about 5 minutes longer.
3. Heat the broiler. Remove the roasting pan from the oven; return the breasts and wings to the pan. Broil the chicken until golden brown, about 2 minutes. Remove the chicken from the pan.
4. Pour off the fat from the roasting pan. Set the pan over moderate heat and add the remaining 1 tablespoon vermouth and the water. Bring to a boil, scraping the bottom of the pan to dislodge any brown bits. Boil until reduced to approximately 2 tablespoons. Add any accumulated juices from the chicken. Spoon the sauce over the chicken.
Variation: If you prefer all white or dark meat, use four bone-in breasts, eight drumsticks, or eight thighs instead of assorted pieces. Cook the breasts for twenty-five minutes or the legs for thirty minutes.
Wine Recommendation: This rustic, herbal roast chicken is best served with a full-bodied and strongly flavored white wine. Look to the south, where the earthy, richly nutty Greco di Tufo is found. Although virtually unknown, it's one of Italy's great whites.