  We predict the existence of a three dimensional quantum Hall effect plateau
in a graphite crystal subject to a magnetic field. The plateau has a Hall
conductivity quantized at $\frac{4e^2}{\hbar} \frac{1}{c_0} $ with $c_0$ the
c-axis lattice constant. We analyze the three-dimensional Hofstadter problem of
a realistic tight-binding Hamiltonian for graphite, find the gaps in the
spectrum, and estimate the critical value of the magnetic field above which the
Hall plateau appears. When the Fermi level is in the bulk Landau gap, Hall
transport occurs through the appearance of chiral surface states. We estimate
the magnetic field necessary for the appearance of the three dimensional
quantum Hall Effect to be $15.4 $T for electron carriers and $7.0 $T for hole
carriers.
