  Let $\phi$ be an isometric automorphism of the non-commutative disc algebra
$\fA_n$ for $n \geq 2$. We show that every contractive covariant representation
of $(\fA_n, \phi)$ dilates to a unitary covariant representation of $(\O_n,
\phi)$. Hence the C*-envelope of the semicrossed product $\fA_n \times_{\phi}
\bZ^+$ is $\O_n \times_{\phi} \bZ$.
