Protecting American Small Business Trade Act of 1998 -Provides that any person who has entered into a contract, license, or other agreement (contract) with a foreign entity before July 1, 1985, that contains a provision to settle any controversy by arbitration shall not be barred from bringing an action in any court of competent jurisdiction in the United States, including any Federal or State court, or from seeking appropriate relief from any U.S. agency to resolve any controversy. Requires actions to be brought under this Act before 180 days after its enactment.