We have measured O in 24 unevolved stars with Keck HIRES observations of the OH lines in the ultraviolet spectral region at high spectral resolution and high signal-to-noise, typically 60-110. The O abundance from OH has been computed by spectrum synthesis techniques for all 24 stars plus the sun. For these cool, unevolved stars we find that O is enhanced relative to Fe with a completely linear relation between [O/H] and [Fe/H] over three orders of magnitude with very little scatter and a slope of +0.66+/-0.02. The relation between [O/Fe] and [Fe/H] is robustly linear and shows no sign of a break at metallicities between -1.0 and -2.0, as has been discussed by others; [O/Fe]=-0.35 (+/-0.03) [Fe/H]. These same results are found whether we use the OH lines from the (0,0) band alone or combine that with the lines from the (1,1) band. We have determined Fe abundances from our UV spectra for the nine stars with [Fe/H]<-2.0 and find excellent agreement with the values found from high-resolution red wavelength spectra.