The anisotropic magnetoresistance (AMR) has been measured at room temperature on a series of epitaxial iron films of various thicknesses. Seven of the films range in thickness from 5 to 20 nm, and one is 500 nm thick. The resistivity of the films was measured with current along photolithographically defined paths parallel to three directions of high symmetry in the single crystal films (, , and ). It was determined that the magnitude of the AMR depends upon the direction the current is applied and that this directional dependence increases with film thickness until saturating near 20 nm. The AMR is roughly 0.15% for all crystal directions in the thinnest films, while in the thickest film, the AMR is 0.08% with current along the  direction, 0.35% along the  direction, and 0.51% along the  direction. These values are to be compared with the AMR of bulk polycrystalline iron which is 0.2%; a weighted average over the different crystallographic directions.