I have long had mixed feelings about Star Trek: Deep Space Nine. On the one hand, it has such fine pedigree, I can't help but be intrigued. On the other, the idea of a "trekking the stars" while aboard a stationary space port seemed a contradiction in terms, and a recipe for boredom.
And yet, a surprisingly high percentage of Trek devotees hold up DS9 as the very pinnacle of the Trek series and the Trek "mission". They will tell you it is the most cerebral, the most philosophical, the most challenging. And, more often than not, they are right. Unlike TOS, TNG, VOY and ENT, DS9 (particularly in its first few seasons) rarely relies on hostile aliens, pyrotechnic space battles and mysterious spatial anomalies threatening its crew to hold the attention of its audience. Warp is NOT a factor on DS9, as it is a series dedicated not to the exploration of the far reaches of space, but to the exploration of the even more inscrutable mysteries of the mind.
"Duet" is the best of the first season, and, arguably, the best episode of the entire series. (Some here have even suggested it may be the best episode of ALL the Trek iterations.) Using clever plot twists, seemingly contradictory clues, and brilliant dialog culminating with a revelation that hits the viewer square in the gut, leaving you quite literally breathless. It is a beautifully written, performed, composed and produced episode.
Others here have revealed enough about the basic plot that I need not restate it; instead, I post this review just to add to the consensus, and let all those considering watching this episode (and this series), that this is amazing television, and far-reaching "exploration" -- even though the space explored is no bigger than that between your ears!