  The recently introduced manifestly covariant canonical quantization scheme is
applied to gravity. New diffeomorphism anomalies generating a multi-dimensional
generalization of the Virasoro algebra arise. This does not contradict theorems
about the non-existence of gravitational anomalies in four dimensions, because
the relevant cocycles depend on the observer's spacetime trajectory, which is
ignored in conventional field theory. Rather than being inconsistent, these
anomalies are necessary to obtain a {\em local} theory of quantum gravity.
