We have undertaken a nine-month study of continuum and emission-line variability in the Seyfert galaxy Mrk 590 in order to determine the structure of the broad-line region. The Hbeta variations are found to lag behind those of the optical continuum by about 19 days. We apply a maximum entropy method to solve for the transfer function which relates the line and continuum variability. This analysis suggests that there is a deficit of emission-line response due to gas along the line of sight to the continuum source, as in the case of NGC 5548, although these data do not allow us to reject with confidence models with significant line-of-sight response. We also show that the Hbeta line variability is apparently confined to the core of the emission line, as suggested previously by Ferland, Korista, and Peterson.