  An asymmetric exclusion process comprising positive particles, negative
particles and vacancies is introduced. The model is defined on a ring and the
dynamics does not conserve the number of particles. We solve the steady state
exactly and show that it can exhibit a continuous phase transition in which the
density of vacancies decreases to zero. The model has no absorbing state and
furnishes an example of a one-dimensional phase transition in a homogeneous
non-conserving system which does not belong to the absorbing state universality
classes.
