Preheat the oven to 400 degrees.

Season the chicken well inside and out with salt and pepper. Put the lemon rind in the cavity. Drizzle the chicken with the oil, and put it in the preheated oven. Turn twice over the next 30 minutes. Reduce the temperature to 350 degrees, then cook for 20 minutes more. Add the onion and shallots to the pan, cook for 10 minutes, then add the wine. Reduce the temperature to 300 degrees, and cook for 15 minutes more (a total cooking time of 1 hour and 15 minutes).

While the chicken cooks, halve the endives lengthwise, brush with 2 tablespoons of melted butter, and place on the broiler. Once they are slightly browned, turn to brown the other side. Remove the endive halves to an oven-safe dish, season with salt and pepper, and add the lemon juice. Put the endives in the oven for 5 minutes, until their hearts are tender.

Remove the chicken from the oven, and reserve its juices (you should have about a cup). Carve the chicken, and arrange on a platter with the endives.

Add the cooking juice from the endives to that of the chicken, and strain into a small bowl. Add the vinegar, stir in the remaining butter, and pour over the chicken. Serve immediately.