Deep Space Nine is host to a delegation of Federation ambassadors and Sisko gives Bashir the "honor" of welcoming them to the station. While Bashir struggles to please the other three dignitaries, Ambassador Lwaxana Troi exclaims that someone has stolen her latinum hair brooch. Although telepathic, she cannot sense guilt from everyone, she points out that Betazoids are unable to read Ferengi minds. Odo deduces that she might be unable to read Dopterians, distant cousins of the Ferengi, and arrests the man who stole her brooch. Lwaxana is instantly infatuated with the Constable.
Lwaxana visits the Security Office and flirts with Odo, who has obviously never been in such a situation. He nervously pretends someone is calling him on the Comm, but she is undeterred. Meanwhile, a mysterious probe-like vessel comes through the Wormhole and the rest of the crew attempt to interface with it. In Sisko's office, Odo asks for advice on how to deal with Lwaxana's aggressive behavior. Explaining he does not have time for "romantic interludes," Odo asks Sisko to do something about Lwaxana, to the Commander's amusement.
As Dax and O'Brien investigate the probe further, Lwaxana approaches Odo about having a picnic and is even more determined to catch his interest; when he informs her that he reverts to a liquid every sixteen hours, she shrugs and responds, "I can swim!" She follows Odo on his way to one of the station's Upper Pylons, but a system failure strands them together in a turbolift. "Alone at last!" Lwaxana declares gleefully.
While trying to repair the station's systems O'Brien discovers that the computer is somehow different. He informs Sisko that the Cardassian computer seems less hostile and has stopped offering opinions on his commands, which is odd. It also seems to break down whenever he is away from it, as if it were a child. The information downloaded from the alien probe is a type of non-sentient life form, which seems to have attached itself to O'Brien like a puppy.
Bashir continues to struggle with the ambassadors and decides to escort them to their quarters until the station is functioning properly. In the meantime, Odo, who initially found Lwaxana's spontaneous nature insufferable, grows less hostile toward her. He grows almost fond of her but appears to be in severe discomfort; as he hesitantly reveals, he is in the fifteenth hour of his regenerative cycle and will soon need to revert to his liquid state.
O'Brien attempts to transfer the alien life form's files back to the probe, and in order to keep the computer from stopping him, he and the rest of the crew give it a list of increasingly complex commands. Something goes awry and a plasma surge creates a fire that traps Bashir and the ambassadors in a corridor. Dax and O'Brien try to establish what went wrong, and O'Brien finally comes to the conclusion that they should build a "doghouse" for their little lost puppy. Containing it may solve their problems.
Back in the turbolift, Odo begins to lose control of his form. Lwaxana tries to be supportive, but he turns away from her and calls it a private matter because no one has ever seen him this way. She hands him her hair - a wig - and tells him no one has ever seen her that way either. Although Odo thinks she looks fine without it, Lwaxana has never cared to be ordinary. When he tells her she is unlike what he expected, she smiles and says that no one has ever paid her a greater compliment. She then lets Odo "melt" in her lap.
O'Brien removes the life form from the station's computer, and upon emerging from a conduit with Bashir, the ambassadors call him a hero. Odo and Lwaxana are rescued from the turbolift; the picnic, Odo points out, was not what Lwaxana had in mind. She tells him the only thing that really matters at a picnic is the company.