"imaginary bad place," 1952, from dys- "bad, abnormal" + ending abstracted from utopia. Earlier in medical use, "displacement of an organ" (by 1844), with second element from Greek topos "place" (see topos). Dystopian was used in the non-medical sense in 1868 by J.S. Mill:
I may be permitted, as one who, in common with many of my betters, have been subjected to the charge of being Utopian, to congratulate the Government on having joined that goodly company. It is, perhaps, too complimentary to call them Utopians, they ought rather to be called dys-topians, cacotopians. What is commonly called Utopian is something too good to be practicable; but what they appear favour is too bad to be practicable. [speech, March 12, 1868]
1551, from Modern Latin Utopia, literally "nowhere," coined by Thomas More (and used as title of his book, 1516, about an imaginary island enjoying the utmost perfection in legal, social, and political systems), from Greek ou "not" + topos "place" (see topos). The current (since c. 1960) explanation of Greek ou "not" is an odd one, as it derives the word from the PIE root *aiw- "vital force, life; long life, eternity." Linguists presume a pre-Greek phrase *(ne) hoiu (kwid) "(not on your) life," with ne "not" + *kwid, an "emphasizing particle" [Watkins]. The same pattern is found elsewhere.
Extended to any perfect place by 1610s. Commonly, but incorrectly, taken as from Greek eu- "good" (see eu-) an error reinforced by the introduction of dystopia (by 1844). On the same model, Bentham had cacotopia (1818).