  We consider the implicit Euler approximation of the stochastic Cahn-Hilliard
equation driven by additive Gaussian noise in a spatial domain with smooth
boundary in dimension $d\le 3$. We show pathwise existence and uniqueness of
solutions for the method under a restriction on the step size that is
independent of the size of the initial value and of the increments of the
Wiener process. This result also relaxes the imposed assumption on the time
step for the deterministic Cahn-Hilliard equation assumed in earlier existence
proofs.
