  We calculate the free energy of a hot gluon plasma to leading order in
hard-thermal-loop perturbation theory. Effects associated with screening, gluon
quasiparticles, and Landau damping are resummed to all orders. The ultraviolet
divergences generated by the hard-thermal-loop propagator corrections can be
cancelled by a temperature-independent counterterm. The deviation of the
hard-thermal-loop free energy from lattice QCD results for T > 2 T_c has the
correct sign and roughly the correct magnitude to be accounted for by
next-to-leading order corrections.
