The Collaborative International Dictionary of English v.0.48:

Clairaudience \Clair*au"di*ence\, n. [F. clair clear + F. & E.
   audience a hearing. See Clear.]
   Act of hearing, or the ability to hear, sounds not normally
   audible; -- usually claimed as a special faculty of
   spiritualistic mediums, or the like.
   [Webster 1913 Suppl.]