The pure rotational spectrum of the FeC radical (X 3 Delta i) has been measured in the laboratory for the first time using millimeter/submillimeter direct absorption techniques. FeC was created by the reaction of iron vapor, produced in a high-temperature Broida-type oven, and methane gas under DC discharge conditions. Six rotational transitions each were recorded for the two lower spin-orbit ladders of this molecule in the frequency range 240--484 GHz, as well as six transitions for the Omega = 3 ladder of the iron isotopomer 54FeC. The data were analyzed using a 3 Delta Hamiltonian, and rotational and certain spin-orbit parameters were determined. The observation of SiC in the circumstellar shell of IRC +10216 suggests that metal carbides such as FeC may be present as well.