The Collaborative International Dictionary of English v.0.48:

Auspice \Aus"pice\, n.; pl. Auspices. [L. auspicium, fr.
   auspex: cf. F. auspice. See Auspicate, a.]
   1. A divining or taking of omens by observing birds; an omen
      as to an undertaking, drawn from birds; an augury; an omen
      or sign in general; an indication as to the future.
      [1913 Webster]

   2. Protection; patronage and care; guidance.
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            Which by his auspice they will nobler make.
                                                  --Dryden.
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   Note: In this sense the word is generally plural, auspices;
         as, under the auspices of the king.
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WordNet (r) 3.0 (2006):

auspice
    n 1: a favorable omen