  A microscopic theory of current partition in fractional quantum Hall liquids,
described by chiral Luttinger liquids, is developed to compute the noise
correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss
geometry, at Laughlin filling factor \nu=1/3, the real time noise correlator
exhibits oscillations which persist over larger time scales than that of an
uncorrelated Hall fluid. The zero frequency noise correlations are negative at
filling factor 1/3 as for bare electrons (anti-bunching), but are strongly
reduced in amplitude. These correlations become positive (bunching) for \nu\leq
1/5, suggesting a tendency towards bosonic behavior.
