The Collaborative International Dictionary of English v.0.48:

Embroilment \Em*broil"ment\, n. [Cf. F. embrouillement.]
   The act of embroiling, or the condition of being embroiled;
   entanglement in a broil. --Bp. Burnet.
   [1913 Webster]

WordNet (r) 3.0 (2006):

embroilment
    n 1: an intricate and confusing interpersonal or political
         situation [syn: imbroglio, embroilment]