  A manifestly super-Poincar\'e covariant formalism for the superstring has
recently been constructed using a pure spinor variable. Unlike the covariant
Green-Schwarz formalism, this new formalism is easily quantized with a BRST
operator and tree-level scattering amplitudes have been evaluated in a
manifestly covariant manner.
  In this paper, the cohomology of the BRST operator in the pure spinor
formalism is shown to give the usual light-cone Green-Schwarz spectrum.
Although the BRST operator does not directly involve the Virasoro constraint,
this constraint emerges after expressing the pure spinor variable in terms of
SO(8) variables.
