The story
From anarcho- + capitalism. Earliest extant attestation is in American author Karl Hess's essay “The Death of Politics”, originally published by Playboy, in March 1969. Even though American economist Murray Rothbard is credited with coining this word, its first possible appearance among his writings is in his 1971 essay “Know Your Rights”, published two years after Hess's essay.
Etymology from Wiktionary, CC BY-SA 4.0.