Nonequilibrium longitudinal optical phonons in a high quality, single crystal wurtzite structure InN sample have been studied by picosecond Raman spectroscopy. Our experimental results demonstrate that the band gap of InN cannot be around 1.89 eV; but are consistent with a band gap of about 0.8 eV. In addition, they disprove the idea that 0.8 eV luminescence observed recently in InN is due to deep level radiative emission in InN.