  Monolayer graphite films, or graphene, have quasiparticle excitations that
can be described by 2+1 dimensional Dirac theory. We demonstrate that this
produces an unconventional form of the quantized Hall conductivity $\sigma_{xy}
= - (2 e^2/h)(2n+1)$ with $n=0,1,...$, that notably distinguishes graphene from
other materials where the integer quantum Hall effect was observed. This
unconventional quantization is caused by the quantum anomaly of the $n=0$
Landau level and was discovered in recent experiments on ultrathin graphite
films.
