  We present the results of a parsec-scale polarization study of three FRI
radio galaxies - 3C66B, 3C78 and 3C264 - obtained with the Very Long Baseline
Array at 5, 8 and 15 GHz. Parsec-scale polarization has been detected in a
large number of beamed radio-loud active galactic nuclei, but in only a handful
of the relatively unbeamed radio galaxies. We report here the detection of
parsec-scale polarization at one or more frequencies in all three FRI galaxies
studied. We detect Faraday rotation measures of the order of a few hundred
rad/m^2 in the nuclear jet regions of 3C78 and 3C264. In 3C66B polarization was
detected at 8 GHz only. A transverse rotation measure gradient is observed
across the jet of 3C78. The inner-jet magnetic field, corrected for Faraday
rotation, is found to be aligned along the jet in both 3C78 and 3C264, although
the field becomes orthogonal further from the core in 3C78. The RM values in
3C78 and 3C264 are similar to those previously observed in nearby radio
galaxies. The transverse RM gradient in 3C78, the increase in the degree of
polarization at the jet edge, the large rotation in the polarization angles due
to Faraday rotation and the low depolarization between frequencies, suggests
that a layer surrounding the jet with a sufficient number of thermal electrons
and threaded by a toroidal or helical magnetic field is a good candidate for
the Faraday rotating medium. This suggestion is tentatively supported by Hubble
Space Telescope optical polarimetry but needs to be examined in a greater
number of sources.
