The Collaborative International Dictionary of English v.0.48:

Wanhope \Wan"hope`\, n. [AS. wan, won, deficient, wanting + hopa
   hope: cf. D. wanhoop. ????. See Wane, and Hope.]
   Want of hope; despair; also, faint or delusive hope;
   delusion. [Obs.] Piers Plowman. "Wanhope and distress."
   --Chaucer.
   [1913 Webster]