  A sample of 129 unresolved radio sources with ultrahigh linear polarization
(>30 per cent) 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. Galaxy
counts within a 1 Mpc radius of the radio sources show that these highly
polarized sources are in environments similar to their low polarization (<2 per
cent) counterparts. Similarly, the line-of-sight environments of the ultrahigh
polarization sources are on average indistinguishable from those of the
low-polarization sources. We conclude that the extraordinarily high average
polarization must be due to intrinsic properties of the sources, such as an
extremely ordered source magnetic field, low internal thermal plasma density or
a preferential orientation of the source magnetic field perpendicular to the
line of sight.
