Fairness in Labor Litigation Act - Amends the National Labor Relations Act to make it an unfair labor practice for an employer or a labor organization, respectively, to bring or cause to be brought any civil or adversarial adjudicatory action against a labor organization or an employer, respectively, if, irrespective of the outcome, such action is determined by a competent fact finder to be frivolous, vexatious, or objectively baseless and not brought in good faith. Makes the party found to have violated this prohibition liable to the party or parties against whom such action is brought for all reasonable costs, fees, and expenses incurred in the defense of such action.