Rinse the chicken thoroughly, and pat dry. Rub the skin and cavity with the lime juice, then sprinkle with salt, pepper, and cayenne; set aside for 15 minutes to let the flavors soak in.
Smear the chicken evenly with the softened butter, and stuff the cavity with onion, garlic, and celery. Place into a pot that is just big enough to hold the chicken, breast-side up. Pour in the bottle of wine, cover the pan, and bring to a boil over high heat. Reduce the heat to medium-low, and gently simmer the chicken until tender, 1 to 1 1/2-hours.
When the chicken has cooked, remove it, and continue simmering the broth. Melt 2 tablespoons of butter in a saucepan over medium heat. Stir in the shallots and garlic, cook until the shallots soften, and turn translucent. Strain the chicken broth through a fine mesh sieve, and add to the shallots.
Pour in the brandy, and bring to a boil over high heat. Reduce heat to medium, then simmer for 10 to 15 minutes. While the sauce is simmering, remove the vegetables from the cavity of the chicken and discard. Remove the breast meat, legs, and any other meat remaining on the bones.
To serve, cut the breast into 1/2-inch thick slices, and separate the legs into drumsticks and thighs. Arrange the chicken on a serving dish, and bathe with the sauce.