The pure rotational spectrum of the FeF radical in its (6) Delta(i) ground electronic state has been recorded using millimeter/submillimeter direct absorption techniques. Transitions arising from all six spin-orbit components have been observed in the nu = 0, 1, and 2 vibrational levels of (FeF)-Fe-56, the main isotopic species, and also in the less abundant Fe-54 isotopomer. Hyperfine splittings, arising from the F-19 nuclear spin of I = 1/2, were resolved in the majority of transitions recorded, and lambda-doubling interactions were observed in the Omega = 3/2, 1/2, and -1/2 spin-orbit ladders. The complete data set has been analyzed using a (6) Delta Hamiltonian, and rotational, spin-orbit, spin-spin, lambda-doubling, and hyperfine constants determined. This study has conclusively demonstrated that the ground electronic state of FeF is (6) Delta(i). It also suggests that FeF has more covalent character to its bonding than alkaline earth or alkali metal counterparts.