Prior to an important conference at U.N.C.L.E. headquarters, a bizarre series of events occurs revolving around a strange man Mr. Hemmingway (Richard Haydn) who keeps appearing and disappearing at will in the building. Solo and Illya learn that he has been placed there by Waverly to test the security system, but THRUSH also has an inside agent, Riley (Peter Haskell), who plants an exploding false tabletop on the conference table at the direction of Dr. Egret (Lee Meriwether). Solo has only a few minutes, before the conference is to begin, to try and find out who the infiltrator is.
