Third in order of being shown, this episode was actually the first one filmed that involved Captain Kirk (the first filmed was "The Cage", which we will see later as the only two-parter episode "The Menagerie" and which had a rather different cast).
In this episode, the Enterprise is on a mission to reach, and perhaps pass, the edge of the Galaxy. On the way, they encounter a damaged emergency beacon/buoy from another vessel, the Valiant, which had been swept in this direction by a space storm of some sort; the damaged final entries of the log beacon indicate that the crew were frantically researching information on ESP (psychic powers), and the final order of the captain appears to have been to self-destruct the vessel.
Continuing on, the Enterprise finds that the edge of the Galaxy has some kind of energy barrier around it, and upon attempting to penetrate the barrier suffers a number of ill effects; most drastically, Lt. Commander Gary Mitchell (an old friend of Kirk's from the Academy) and ship's psychologist Elizabeth Dehner collapse suddenly. The Enterprise backs out of the barrier, its warp engines damaged and in need of repair; several people on the ship have collapsed and die. Mitchell has survived, but when he awakens, his eyes have acquired an eerie silver glow.
At first this appears to be the only effect, but as time goes on, it becomes clear that the encounter with the Barrier has done something else to Gary Mitchell; first he simply seems to be more sensitive to events and actions around him, quicker-witted (one scene shows him reading at an ever-increasing speed), but soon he begins to manifest additional abilities, including control of bodily functions, telekinesis, and even clairvoyance and possibly telepathy. Along with these additional abilities, he appears to be developing a dangerous level of megalomania.
The Enterprise is proceeding to the only planet within impulse power range, a lithium-cracking station on Delta Vega. Despite numerous indications that Gary is becoming a danger to the crew and the ship, Captain Kirk is reluctant to accept that this is really the case. Gary has been his friend for years and it's difficult to admit that his worst tendencies have been given free rein by this strange effect. Eventually, however, Kirk has to admit that there isn't much choice; if he doesn't do something soon, he may be forced to the same decision as the captain of the Valiant.
The decision is made to maroon Mitchell on Delta Vega; it's a better choice than killing him, or so Kirk hopes. Despite Mitchell's growing powers, they do manage to subdue him and beam him down. However, even though they set up a special force-field holding cell, it doesn't appear they can hold him long. In fact, they can hold him even less than they think; Mitchell manages to kill one of the crew from long-distance, strangling him with a telekinetically-controlled cable, so that a final detonation switch can't be used against him. He is then able to break out, and it is revealed that Dr. Dehner -- who had been arguing against marooning Mitchell -- has been affected similarly to Gary, as her eyes have now become silver as well.
Having lost a crewmember and had the others nearly killed as well, Kirk sets out to finish this armed with a phaser rifle -- and with direct orders to his crew to leave the area at maximum speed if he does not report back in a few hours. By this time Mitchell is powerful enough to perform feats that are effectively magical and is thinking of himself as a god. Dehner, however, is not quite as affected by megalomania, and when she encounters Kirk, he appeals to her humanity, and specifically to her professional psychological opinion: "Look at Mitchell! Look at the symptoms! What's your prognosis, doctor?"
Mitchell confronts Kirk and shows him the tomb he's already created for his "old friend". But before he can kill the Captain, Dehner strikes, apparently having come to the conclusion that Kirk is right about Mitchell... and perhaps about her, if things continue. The battle between the two super-psychics is enough to temporarily drain Mitchell's power and Kirk is able to gain the upper hand temporarily, until Gary starts to recover; however, before his powers fully return, Kirk retrieves his phaser rifle and triggers a giant rockfall on top of Mitchell, killing him. Dehner dies of injuries inflicted by Mitchell. Kirk records both as "killed in the line of duty", rather than have his friend's memory sullied by an event which was, in the end, unpredictable and not in his control.
Overall, this is a stronger episode than "Charlie X", and in some ways better than "Man Trap". It is clear that this was filmed earlier (costumes are different, as are sets, and many of the main cast are not present yet). Seen immediately after "Charlie X", however, one does hope that "megalomanic super-psis" won't be in every episode; it's in danger of becoming a theme.
The revised special effects shine in this episode, especially the carefully reconstructed CGI Enterprise used for exterior shots and the cloud-curtain design of the Galactic Barrier.
Overall, a good episode which moves well. I remembered this one fondly and it did not disappoint, although some of the dialogue -- especially in the early scenes -- hasn't aged as well as it might.