Litigation Abuse Reform Act of 1986 - Amends the Federal Rules of Civil Procedure to provide certain limitations and procedures regarding civil damages in actions alleging negligence, strict or product liability, intentionally tortious conduct, or malpractice by a physician, accountant, lawyer, architect, engineer, or other professional. Requires that future damage awards exceeding $100,000 be made by periodic payments. Requires that damage awards be offset by an amount received as compensation for the same injury from other sources. Limits the amount of damages for noneconomic losses to $100,000. Establishes a contingency fee schedule for plaintiffs' attorneys. Permits the awarding of punitive damages only where the conduct of the defendant manifests a conscious disregard for safety. Provides that punitive damages awarded in any civil action to which this Act applies shall be paid to the clerk of the court and transmitted to the Treasurer of the United States, for the use of the Administrative Office of the United States Courts and the Federal Judicial Center. Makes any attorney whose conduct is calculated for delay, or is found to be in bad faith, subject to pecuniary sanctions by the court.