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 2pi. 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.