The Collaborative International Dictionary of English v.0.48:

Trilemma \Tri*lem"ma\, n. [NL., fr. Gr. ? (see Tri-) + ? any
   thing received, in logic, an assumption. Cf. Dilemma.]
   1. (Logic) A syllogism with three conditional propositions,
      the major premises of which are disjunctively affirmed in
      the minor. See Dilemma.
      [1913 Webster]

   2. A state of things in which it is difficult to determine
      which one of three courses to pursue.
      [1913 Webster]