A search using the Very Large Array was performed for 1720-megahertz OH maser line emission from a number of nonthermal radio continuum sources in the galactic center region. The 1720-megahertz transition has recently been noted for its potential as a tracer of shock activity. The most striking result was the detection of extended 1720-megahertz OH maser emission, as well as a number of compact OH maser features, along the interface between a large-scale continuum shell (G359.1-0.5) and its surrounding ring of high-velocity molecular gas. The morphological correlation among the neutral gas, the nonthermal shell, and the maser features provides strong support for the hypothesis that the 1720-megahertz maser line of OH arises from gas shocked by the impact of the expanding supernova remnant into the molecular material. However, the radial velocities of the molecular cloud surrounding G359.1-0.5 are more negative than that of the OH maser spots by more than 50 kilometers per second. Here it is suggested that only the low-radial-velocity component of the carbon monoxide material at the limb of the remnant satisfies the physical conditions required for collisional pumping of the OH 1720-megahertz line behind the expanding shock front.