This adjective refers to people and things that belong to or inhabit the underworld.
The biggest problem with it, once you’ve worked out how to spell it, is how to say it. American dictionaries suggest that the initial ch should be silent, while most British ones say that it should be said as k, reflecting the Greek source, khthon, earth. No such ambiguity exists with another word from the same source, autochthon, an original inhabitant of any country, who seems to have sprung from the soil; here the ch is said as k.
The classic Greek word referred not to the surface of the ground, which would be gaia, but to what lies underneath. Both gaia and khthon were associated with the supernatural beings that dwelled in these domains, Gaia being the personification of the Earth and the original mother of all beings, while the deities of chthonic realms were Pluto and Persephone.
The English word is comparatively new, from the late nineteenth century. It has flowered as a favourite term of SF and fantasy writers. “Like the rumble of a live volcano it came,” wrote Piers Anthony in his 1985 collection of short stories, Anthonology, “throbbing up from the fundament, pressuring chthonic valves, gathering into an irresistible swell.” One of Charles Stross’s characters was heavily sarcastic with its help in The Jennifer Morgue:
“Really?” asks the woman. “Are you sure it’s all over?” Billington glances at her. “Pretty much, apart from a few little details — mass human sacrifices, invocations of chthonic demigods, Richter-ten earthquakes, harrowing of the Deep Ones, rains of meteors, and the creation of a thousand-year world empire, that sort of thing. Trivial, really.”
The Deep Ones, by the way, are frog-like creatures from the imagined world of H P Lovecroft that’s usually referred to as the Cthulhu Mythos. It’s said that Lovecraft took the name of Cthulhu, his enormous alien god creature, from khthon. Certainly, Lovecraft did a lot to popularise chthonic and it’s through his influence that it remains so popular in SF.