In the second episode of The Queen's Gambit, from Wikipedia's summary:

After her overdose, Beth is forbidden to play chess. Time passes and Beth is adopted as a teenager by suburban couple Alma and Allston Wheatley. Allston is emotionally distant and frequently leaves for "business trips"; it soon becomes clear that their marriage is not a happy one. At her new high school, Beth is bullied by the popular girls from the "Apple Pi Club" for her drab clothes. Beth discovers her adoptive mother is taking the same tranquilizer pills that she was given at the orphanage and secretly steals some for herself, allowing her to play mental chess again. She also steals a chess magazine and learns about the upcoming Kentucky State Championship. She writes to Mr. Shaibel, who sends her the money for the entrance fee. As she cruises through her games, she develops a crush on one of her opponents, a young man named Townes. After the second day of the tournament, during which her periods start, Beth comes home to find that Allston has deserted them. Beth fears that she will be sent back to the orphanage, but Alma tells her they will lie so she can stay. During her final game of the tournament against Harry Beltik, the highest-ranked player, Beth becomes flustered and runs to the restroom, where she takes a tranquilizer pill, then wins the game. Upon learning of the prize money on offer in a tournament in Cincinnati, Alma hatches a plan for the two women to support themselves.

(emphasis mine)

I'm aware that there is some kind of anti-doping tests in chess, but I do not know what the tests test for. Does taking tranquilizers count as cheating in chess?

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    Of course, the rules have probably changed between the 60s and now. – Acccumulation Jan 14 at 0:57

The World Chess Federation (FIDE) uses the list of prohibited substances published by the World Anti-Doping Agency.

I did not see tranquilizers on the list, although I can't say I'm familiar enough with the names of medications to know for sure.

Tranquilizers would seem to be a rather counterproductive way to cheat in most sports, which might explain why they're not on the list.

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    "Tranquilizers would seem to be a rather counterproductive way to cheat in most sports ..." - There might be surprising exceptions though. I'd expect people to say the same of alcohol, but alcohol is actually prohibited in pro archery competitions because of performance enhancing effects. No idea about tranquilizers and chess though. – marcelm Jan 13 at 13:45
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    Tranquilizers as in mild sedatives could work to reduce anxiety, which could be a factor in chess. I don't see them mentioned in the WADA list either. But I do see methylphenidate (an ADHD drug) listed as forbidden in all sports, and beta blockers (can lower heart rate and tremors, used for stage fright) forbidden in shooting, archery, billiards and such. – ilkkachu Jan 13 at 13:45
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    While anti-doping rules are usually framed in terms of "performance-enhancing drugs", that's not always the motivation for prohibiting some substances. Some are prohibited for moral reasons, as competitors are considered role models. E.g. marijuana is not considered performance-enhancing (except, like tranquilizers, for reducing stress), but it's on the prohibited substance list. – Barmar Jan 13 at 16:32
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    @Barmar: I rather suspect marijuana is on the list because, several decades ago, the US decided that it was Bad with a capital B, and not for any rational reason. – Kevin Jan 13 at 17:20
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    @Kevin Exactly, that's what I mean by "moral reasons". – Barmar Jan 13 at 17:26

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