Some extragalactic supernovae, such as SN 1986J in NGC 891 (Rupen et al. 1987), are unusually strong radio sources. Their radio emission typically peaks a few years after the supernova explodes, and appears to arise from the interaction of the supernova shock with a dense stellar wind shed by the progenitor star. Since two radio-loud and possibly optically faint supernovae have recently been found serendipitously in nearby spiral galaxies, it is possible that such objects are common. If so, this would have important consequences for our understanding of both the chemical enrichment history of galaxies and the radio emission from starburst galaxies. Preliminary results from a survey of nearby spiral galaxies with the Molonglo Observatory Synthesis Telescope (MOST) allow us to make a first estimate of the radio supernova rate. A larger study now in progress will provide a much more sensitive measurement.