  We derive an effective two-dimensional Hamiltonian to describe the low energy
electronic excitations of a graphite bilayer, which correspond to chiral
quasiparticles with a parabolic dispersion exhibiting Berry phase $2\pi$. Its
high-magnetic-field Landau level spectrum consists of almost equidistant groups
of four-fold degenerate states at finite energy and eight zero-energy states.
This can be translated into the Hall conductivity dependence on carrier
density, $\sigma_{xy}(N)$, which exhibits plateaus at integer values of
$4e^{2}/h$ and has a ``double'' $8e^{2}/h$ step between the hole and electron
gases across zero density, in contrast to $(4n+2)e^{2}/h$ sequencing in a
monolayer.
