  We obtain a manifestly background independent BRST quantization of the $\N=4$
supersymmetric spinning particle. We show that nilpotency of the BRST charge
$Q$ implies the Einstein equations admitting a cosmological constant of
indefinite sign. The physical graviton states are given by the vertex operator,
obtained by an infinitesimal variation of $Q$, acting on diffeomorphism ghost
states. In addition, the tree-point graviton scattering vertex is correctly
reproduced by the worldline computation with these vertex operators.
