The USS Enterprise heads to Torona IV to open negotiations with the insectoid Jaradan race on behalf of the Federation. The Jaradan are meticulous on procedure, and when the Federation last attempted to negotiate twenty years ago, a simple mispronunciation in the Federation's greeting led to the Jaradan refusal to talk until the present. Captain Picard has been given the honor to give the greeting, but rehearsing the statement has become tiring and opts to spend some time in the holodeck in a Dixon Hill story. On the holodeck, as Detective Hill, Picard takes up the case of Jessica Bradley, who believe Cyrus Redblock is trying to kill her. Picard leaves the holodeck to continue the program later, and affirms the Enterprise's estimated arrival at Torona. Picard offers both Dr. Crusher and visiting historian Dr. Whalen to join him on his next visit to the holodeck. While Dr. Crusher is still preparing, Picard and Whalen are ready to enter the holodeck when Data, also dressed in period pieces, arrives, having overheard Picard's invitation. Entering the holodeck, the three discover that Jessica has been murdered, and when Picard explains that she was at his offices the day before, they are arrested by police officer McNary on suspicion of her murder. As they are taken away, Dr. Crusher enters the holodeck and joins her friends when they arrive at the police station.
Meanwhile, as the Enterprise enters communication range of the Jaradan, they are hailed by the beings, causing a momentary flicker of power. The Jaradan demand their greeting, and are somewhat insulted at having to talk to anyone else but the Captain. The crew try to communicate with Picard in the holodeck but find it impossible, and quickly realize the holodeck's functions have been affected by the Jaradan signal, preventing them from even opening the doors to the room. LaForge and Wesley set to work on repairing the holodeck systems.
Inside the holodeck, the group are let free from their police interrogation and return to Dixon's office. There, Mr. Leech waits for Picard, demanding he turn over an object Jessica had given him. When Picard fails to understand, Leech shoots Dr. Whalen with a gun. As Dr. Crusher attempts to care for him, Picard and Data quickly recognize the holodeck is malfunctioning, its safety protocols disabled, and they are unable to leave. Mr. Leech is shortly joined by Redblock and continues to demand the object. Officer McNary also becomes involved in the standoff, having been wanting to follow up on the previous interrogation. Picard attempts to explain the nature of the holodeck but Redblock refuses to believe him.
Outside, Wesley finds that the holodeck may have converted the trapped crew as holographic signals, and cannot simply turn off the system for fear of losing them. Instead, he opts to reset the simulation, briefly causing Picard and the others to be in the environs of the middle of a winter storm before finding themselves back in Dixon's office. The reset, however, successfully cleared the malfunction, and the exit doors appear. Redblock and Leech, believing the doors to lead to a new world to ransack, exit the holodeck despite Picard's warnings and find themselves disintegrating as they were only holographic elements. Picard thanks McNary for his assistance but tells him this is the "big goodbye" as they leave the holodeck. Dr. Crusher races Dr. Whalen to Sick Bay while Picard is able to get to the bridge just in time to give the proper greeting to the Jaradan. The Jaradan accept the greeting, heralding the start of successful negotiations.