  We consider the stochastic Allen-Cahn equation perturbed by smooth additive
Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$,
and study the semidiscretization in time of the equation by an implicit Euler
method. We show that the method converges pathwise with a rate $O(\Delta
t^{\gamma}) $ for any $\gamma<\frac12$. We also prove that the scheme converges
uniformly in the strong $L^p$-sense but with no rate given.
