  The asymptotic shape theorem for the contact process in random environment
gives the existence of a norm $\mu$ on $\Rd$ such that the hitting time $t(x)$
is asymptotically equivalent to $\mu(x)$ when the contact process survives. We
provide here exponential upper bounds for the probability of the event
$\{\frac{t(x)}{\mu(x)}\not\in [1-\epsilon,1+\epsilon]\}$; these bounds are
optimal for independent random environment. As a special case, this gives the
large deviation inequality for the contact process in a deterministic
environment, which, as far as we know, has not been established yet.
