The pure rotational spectrum of cobalt monofluoride in its X (3)Phi(i) electronic state has been measured in the frequency range of 256-651 GHz using direct absorption techniques. CoF was created by reacting cobalt vapor with F(2) in helium at low pressure (25-30 mTorr). All three spin components were identified in the spectrum of this species, two of which exhibited lambda doubling. Each spin component showed hyperfine splittings from both nuclei: an octet pattern arising from the (59)Co spin of I=72, which is further split into doublets due to the (19)F nucleus (I=12). The data were fitted close to experimental precision using an effective Hamiltonian expressed in Hund's case (a) form, and rotational, fine structure, hyperfine, and lambda-doubling parameters were determined. There is evidence that the rotational levels of the highest spin component (3)Phi(2) are perturbed. The r(0) bond length of CoF was estimated from the rotational constant to be 1.738 014(1) A. This value is in good agreement with previous studies but much more accurate. The matrix elements necessary for the complete treatment of Lambda doubling in a Phi state have been derived and are presented for the first time.