Gun Show Loophole Closing Act of 2017 This bill makes it unlawful for any person to operate a gun show unless such person: (1) has attained 21 years of age; (2) is not prohibited from transporting, shipping, or receiving firearms and has not violated any federal firearms requirements; (3) has registered with the Department of Justice (DOJ) as a gun show operator and has provided a photograph and fingerprints; (4) has not concealed material information nor made false statements in connection with a gun show operator registration; and (5) notifies DOJ of the date, time, and duration of a gun show not later than 30 days before the commencement of such show and verifies the identity of each vendor at the gun show. The bill makes it unlawful for a person not licensed under this bill to transfer possession of a firearm at a gun show to another person not licensed unless a licensed importer, manufacturer, or dealer has, among other conditions, recorded the transfer with DOJ. Additionally, the licensed dealer must notify the prospective transferor and transferee of the firearm that the national instant criminal background check system has provided the dealer with a unique identification number indicating that the receipt of the firearm would not violate certain federal or state firearm laws. The bill grants DOJ authority to enter, without a showing of reasonable cause or a warrant, any place where a gun show is held or where a gun show operator is required to maintain records to examine records and inventory to determine compliance with this bill.