Place chicken in a shallow nonaluminum dish and add 1/4 cup lime juice. Toss lightly, cover and marinate for 30 minutes in the refrigerator. Drain and reserve the marinade.
Combine shallots, 1 1/2 teaspoons tarragon, 1 1/2 teaspoons cilantro, 1/4 teaspoon salt and black pepper in a small bowl. Spread 2 teaspoons of the mixture at the base of each chicken breast and roll up. Using two pieces of butcher's string, one running horizontally and one vertically, tie each breast into a package.
Combine water, the remaining 1/4 cup lime juice, 2 tablespoons tarragon, 2 tablespoons cilantro, 1/4 teaspoon salt, reserved marinade, sherry, crushed red pepper and bay leaves in a large high-sided skillet. Bring to a boil, reduce heat to low, add the chicken, cover and poach gently until no longer pink inside, 20 to 25 minutes.
Equipment: Kitchen string
Note: Sherry is a type of fortified wine originally from southern Spain. Don't use the “cooking sherry” sold in many supermarkets—it can be surprisingly high in sodium. Instead, purchase dry sherry that's sold with other fortified wines in your wine or liquor store.