In a 1-quart saucepan, bring the broth and litchis to a boil over medium heat. Reduce the heat to low and cook until the sauce is reduced by about half. Let cool slightly.
Process the berry mixture in a blender or food processor until smooth; return the mixture to the pan. Add water to berry mixture. Cook over low heat, stirring constantly, until the litchi puree thickens, about 1 minute. Cover and set aside.
In a medium bowl, combine the mustard and honey. Coat the chicken evenly on both sides with the mustard mixture.
In a non-stick skillet, warm the oil over high heat. Add the chicken and cook until it is well browned on both sides and no longer pink. Serve with the litchi puree.