A sample of 129 unresolved radio sources with ultrahigh linear polarization (>30%) has been selected from the NRAO VLA Sky Survey. Such high average linear polarization is unusual in extragalactic sources. Higher resolution Australia Telescope Compact Array and Very Large Array observations confirm the high average polarization but find that most of these sources are extended. The Sloan Digital Sky Survey spectroscopy, where available, shows that the optical counterparts are elliptical galaxies with no detectable emission lines. The optical spectra, radio luminosity, linear size and spectral index of these sources are typical of radio-loud active galactic nuclei.