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Adverb: by chance
  1. By accident; fortuitously
    "betrayed by a word by chance overheard";
    - haply [archaic], by luck
     
  2. Without advance planning
    "they met by chance";
    - accidentally, circumstantially, unexpectedly
     
  3. [archaic] Through chance
    "To sleep, by chance to dream...";
    - perchance [archaic]

Antonym: on purpose

Encyclopedia: By chance