  We study a non-conserved one-dimensional stochastic process which involves
two species of particles $A$ and $B$. The particles diffuse asymmetrically and
react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA
\leftrightarrow A\emptyset$ and $B\emptyset \leftrightarrow BB \leftrightarrow
AB \leftrightarrow B\emptyset$. We show that the stationary state of the model
can be calculated exactly by using matrix product techniques. The model
exhibits a phase transition at a particular point in the phase diagram which
can be related to a condensation transition in a particular zero-range process.
We determine the corresponding critical exponents and provide a heuristic
explanation for the unusually strong corrections to scaling seen in the
vicinity of the critical point.
