The X-ray light curves in the 0.4-1.5 keV and 2-7 keV bands of the RS CVn binary AR Lacertae observed on 1993 June 1-3 over one full orbital cycle with the ASCA satellite have been used to map the spatial structure of AR Lac's coronae. We find that both stars are X-ray active, that the corona of the K-type secondary star appears to be hotter than that of the G-type primary star, that X-ray emission is concentrated on the sides of the stars facing each other, and that there are compact and well-localized regions of enhanced X-ray emission with heights much smaller than the stellar radii. In one class of solutions there are additional extended regions with dimensions similar to or greater then the radii of the underlying stars which may be structures that interconnect the two stars. There are also other acceptable models without extended structures, however our analysis indicates that solutions with extended sources are more probable. Also, about 50% of the X-ray emission is unmodulated and could come from either an extended halo region, from the poles of the larger K star, or from other symmetric or uneclipsed structures in the orbital plane. We compare the coronal structures inferred from the ASCA observations with those inferred using the same technique from an EXOSAT observation of AR Lac made in 1984 and find that there are substantial differences between the coronal structures at these two epochs. For the solution with extended material in the orbital plane, we have derived the rough physical parameters for the X-ray-emitting plasma, using the derived information on the spatial sizes of the various spatial components together with information about the emission measure and temperatures obtained from a simple spectral analysis of the ASCA data.