The Collaborative International Dictionary of English v.0.48:

Compline \Com"pline\, Complin \Com"plin\, n. [From OE. complie,
   OF. complie, F. complies, pl., fr. LL. completa (prop. fem.
   of L. completus) the religious exercise which completes and
   closes the service of the day. See Complete.] (Eccl.)
   The last division of the Roman Catholic breviary; the seventh
   and last of the canonical hours of the Western church; the
   last prayer of the day, to be said after sunset.
   [1913 Webster]

         The custom of godly man been to shut up the evening
         with a compline of prayer at nine of the night.
                                                  --Hammond.
   [1913 Webster]

WordNet (r) 3.0 (2006):

compline
    n 1: last of the seven canonical hours just before retiring
         [syn: compline, complin]