  We consider the problem of metastability in a probabilistic cellular
automaton (PCA) with a parallel updating rule which is reversible with respect
to a Gibbs measure. The dynamical rules contain two parameters $\beta$ and $h$
which resemble, but are not identical to, the inverse temperature and external
magnetic field in a ferromagnetic Ising model; in particular, the phase diagram
of the system has two stable phases when $\beta$ is large enough and $h$ is
zero, and a unique phase when $h$ is nonzero. When the system evolves, at small
positive values of $h$, from an initial state with all spins down, the PCA
dynamics give rise to a transition from a metastable to a stable phase when a
droplet of the favored $+$ phase inside the metastable $-$ phase reaches a
critical size. We give heuristic arguments to estimate the critical size in the
limit of zero ``temperature'' ($\beta\to\infty$), as well as estimates of the
time required for the formation of such a droplet in a finite system. Monte
Carlo simulations give results in good agreement with the theoretical
predictions.
