We present high spatial resolution 21cm HI observations of EA01A and EA01B, a pair of interacting post-starburst, or E+A, galaxies at z = 0.0746. Based on optical HST/WFPC2 images, both galaxies are known to display disturbed morphologies. They also appear to be linked by a bridge of stars. Previous HI observations Chang et al. (2001) had already uncovered sizable quantities of neutral gas in or near these galaxies but they lacked the spatial resolution to locate the gas with any precision within this galactic binary system. We have analysed deep, high resolution archival VLA observations of the couple. We find evidence for three gaseous tidal tails; one connected to EA01A and two emanating from EA01B. These findings confirm, independently from the optical imaging, that (i) EA01A and EA01B are actively interacting, and that, as a consequence, the starbursts that occurred in these galaxies were most likely triggered by this interaction, and that (ii) 6.6+-0.9 10^9 Msun of neutral gas are still present in the immediate vicinity of the optical bodies of both galaxies. The HI column density is lowest at the optical positions of the galaxies, suggesting that most of the neutral gas that is visible in our maps is associated with the tidal arms and not with the galaxies themselves. This might provide an explanation for the apparent lack of ongoing star formation in these galaxies.