A far-infrared absorption line has been observed in antiferromagnetic FeF2 at 154.4 cm-1. The absorption is greatest when the electric-field vector of the radiation is polarized parallel to the crystal c axis. The line broadens and shifts to lower frequencies as the temperature is raised, disappearing above the Néel temperature. The line strength is comparable to that of the antiferromagnetic resonance line observed at 53 cm-1. The line does not disappear as T→0, nor does it appear to broaden, shift, or split in a magnetic field. A theory based on a phenomenological spin Hamiltonian is presented which explains many of the properties of the line in terms of a two-magnon absorption process which predicts a line at 154 cm-1 in excellent agreement with experiment. Another phenomenological theory of the same line by Moriya and the relationship of the present work to that of Allen, Loudon, and Richards on MnF2 are discussed. The spin Hamiltonian used in this work is microscopically derived in the following paper.