We propose an experiment to probe the unconventional quantum statistics of quasiparticles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for backscattering. Thermal fluctuations of the number of quasiparticles enclosed between the two point contacts introduce current noise, which reflects the statistics of the quasiparticles. We analyze Abelian nu=1/q states and the non-Abelian nu=5/2 state.