  This paper introduces a position-space renormalization-group approach for
nonequilibrium systems and applies the method to a driven stochastic
one-dimensional gas with open boundaries. The dynamics are characterized by
three parameters: the probability $\alpha$ that a particle will flow into the
chain to the leftmost site, the probability $\beta$ that a particle will flow
out from the rightmost site, and the probability $p$ that a particle will jump
to the right if the site to the right is empty. The renormalization-group
procedure is conducted within the space of these transition probabilities,
which are relevant to the system's dynamics. The method yields a critical point
at $\alpha_c=\beta_c=1/2$,in agreement with the exact values, and the critical
exponent $\nu=2.71$, as compared with the exact value $\nu=2.00$.
