The Collaborative International Dictionary of English v.0.48:

Precociousness \Pre*co"cious*ness\, Precocity \Pre*coc"i*ty\, n.
   [Cf. F. pr['e]cocit['e].]
   The quality or state of being precocious; untimely ripeness;
   premature development, especially of the mental powers;
   forwardness.
   [1913 Webster]

         Saucy precociousness in learning.        --Bp.
                                                  Mannyngham.
   [1913 Webster]

         That precocity which sometimes distinguishes uncommon
         genius.                                  --Wirt.
   [1913 Webster]

WordNet (r) 3.0 (2006):

precociousness
    n 1: intelligence achieved far ahead of normal developmental
         schedules [syn: precociousness, precocity]