The Collaborative International Dictionary of English v.0.48:

Peculiarity \Pe*cul`iar"i*ty\ (p[-e]*k[=u]l`y[a^]r"[i^]*t[y^]),
   n.; pl. Peculiarities (p[-e]*k[=u]l`y[a^]r"[i^]*t[i^]z).
   1. The quality or state of being peculiar; individuality;
      singularity. --Swift.
      [1913 Webster]

   2. That which is peculiar; a special and distinctive
      characteristic or habit; particularity.
      [1913 Webster]

            The smallest peculiarity of temper or manner.
                                                  --Macaulay.
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   3. Exclusive possession or right. [Obs.] --Bp. Hall.
      [1913 Webster]

WordNet (r) 3.0 (2006):

peculiarity
    n 1: an odd or unusual characteristic [syn: peculiarity,
         distinctive feature, distinguishing characteristic]
    2: a distinguishing trait [syn: peculiarity, specialness,
       specialty, speciality, distinctiveness]
    3: something unusual -- perhaps worthy of collecting [syn:
       curio, curiosity, oddity, oddment, peculiarity,
       rarity]