  We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of
long-term correlated noise. By means of extensive numerical simulations of
models in the KPZ universality class we find that, as the noise correlator
range increases, the surface develops a pattern of macroscopic facets that
completely dominate the dynamics and induce anomalous kinetic roughening. This
novel phenomenon is not described by the conventional dynamic renormalisation
group calculations and can explain the singular behavior observed in the
analytical treatment of this problem in the seminal paper of Medina {\it et al}
[Phys. Rev. A {\bf 39}, 3053 (1989)].
