Paris has a vision of the last moments of a murder victim's life, who he's just been convicted of killing. He's told that he'll relive the vision once every 14 hours. Justice is a harsh mistress. After the title sequence, Kes and the HoloDoc are in sick bay, discussing a possible name. So is this before or after the pre-credits sequence? HoloDoc tries a few names.
Janeway alerts the HoloDoc to an incoming damaged shuttle, which carries Kim. Harry reports that Paris has been convicted of the murder of a scientist they were working with. He invited them to his home for dinner. Apparently his wife didn't bother changing out of her nightie. Anyway, once Harry and the professor started geeking about sciency stuff, Paris got bored and wandered off, apparently to bone the professor's wife and later off the professor. As you do.
Unconvinced, Janeway sets course for the planet in question. They're greeted as they enter the system by a ship from the race which is at war with the bunch who've convicted Paris. The other aliens warn them not to get involved in the war. Exciting.
They proceed to the planet, where Janeway and Tuvok are told that Paris was convicted by the victim's last memories. Paris denies killing the prof, but admits that he hung out with the professor's wife a bit. Then he has another spell and falls unconscious. Janeway convinces the locals to let them beam up with him, so the Holodoc can check him out.
HoloDoc says that the repeating memories are causing neurological damage. Tuvok decides to investigate further, and visits the wife. Wife could not be more suspicious if she was having a party, but she repeats the story of how Paris offed her husband. Back on Voyager, Paris confirms her story, but doesn't remember the bit about killing the prof.
They're interrupted by Voyager being attacked by the other aliens. Chakotay uses the old "play dead" trick and disables both attacking vessels.
Tuvok does a mind meld with Paris so he can witness the crime himself which, apparently, gives him more clues. Kim and Paris set off on a shuttle back to the planet, and are intercepted by the other aliens, who identify Paris. Voyager promptly beams Kim and Paris off, and then forces them to return the shuttle.
Tuvok calls a meeting at the scene of the murder, and points out that the murder in the memories was the same height as the prof's wife, yet Paris is taller than her. Also, the symbols overlayed on the vision are actually weapons research, intended to be smuggled to the other side. As it turns out, the real murderer is the doctor who implanted the memories. Way to not get caught, dude.