We present the first results from our GALEX program designed to obtain ultraviolet (UV) spectroscopy of nearby core-collapse supernovae (SNe). Our first target, SN 2005ay in the nearby galaxy NGC 3938, is a typical member of the II-P SN subclass. Our spectra show remarkable similarity to those of the prototypical type II-P event SN 1999em, and resemble also Swift observations of the recent type II-P event SN 2005cs. Taken together, the observations of these three events trace the UV spectral evolution of SNe II-P during the first month after explosion, as required in order to interpret optical observations of high-redshift SNe II-P, and to derive cross-filter K-corrections. While still highly preliminary, the apparent UV homogeneity of SNe II-P bodes well for the use of these events as cosmological probes at high redshift.