Quantum Monte Carlo calculations of the ground state energies of the fluorine atom and the hydrogen fluoride molecule have been carried out using both fixed-node and released-node methods. The fixed-node total energies for both F and FH are among the most accurate available. The fixed-node dissociation energy D-e = 141.3(4) kcal mol(-1) is in excellent agreement with experimental data. The cancellation of the nodal error was achieved with trial wave functions having nodal surfaces determined by Slater determinants of the near Hartree-Fock limit quality. With the released-node Green’s function quantum Monte Carlo method the lowest upper bounds to the ground state energies to date for both F [E(0) = -99.731(4) Hartree] and FH [E(0) = -100.458(5) Hartree] have been obtained.