Crime in Antarctica is relatively rare, given the lack of humans to commit crime against and the lack of legislation against penguins that can be used to punish them for their terrible crimes.
However, with the extreme monotony and isolation of life at research stations on the continent, there have been a few incidents. This includes in 1984 when one member of an Argentine research team burned down their research station as the final supply ship of the year was leaving so that he didn't have to stay for the winter, and a hammer fight between staff at a US base in 1996.
One unfortunate incident between two Soviet scientists ended with the whole research station being banned from chess, according to several sources.
According to the story, at Russia's Vostok station in 1959, a scientist "became unhinged after losing a game of chess, and murdered his opponent with an axe". According to some sources, this resulted in the Soviet Union (and later Russia) banning the game from taking place in Antarctica or space due to similar levels of isolation.
Though it's a story believed by some who work at research stations, it does have the ring of an urban legend. Details of the incident are scarce, and in some versions, the victim is injured rather than dies. It's also not the case that chess has been banned in space, with one game famously being played between a Russian astronaut and "representatives of Earth" on the ground over the radio. The game ended in a draw, but with zero stabbings we can chalk that up as a success.
In 2018, a similar incident was reported by the media, where 55-year-old electrical engineer Sergei Savitsky stabbed 52-year-old welder Oleg Beloguzov at the Bellingshausen research station. According to tabloids at the time, the incident happened after Beloguzov repeatedly spoiled endings of books that Savitsky was reading before he had time to finish them. That incident had the ring of an urban legend too, and though an incident did take place, the details about book spoilers turned out to be unverified and likely false. Savitsky had mental health problems, with AP citing only "tensions in a confined space" rather than "he said who dies at the end of Wuthering Heights".
While an amusing story/cautionary tale about the effects of isolation, the lack of details on the chess story – as well as news reports from the time – makes us think this is likely an embellishment of an incident, if not a straight-up urban legend. The story appears to have been first mentioned some time in the 1980s according to chess enthusiasts turned sleuths at the Chess stack exchange.
Far from staying away from the game, a five-month chess championship took place between Soviet explorers in Antarctica in 1978. This seems unlikely if, just a few decades earlier, chess was banned because of all the murder.