  Quasi-one-dimensional stochastic Dirac operators with an odd number of
channels, time reversal symmetry but otherwise efficiently coupled randomness
are shown to have one conducting channel and absolutely continuous spectrum of
multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and
Goldsheid-Margulis to the analysis of random products of matrices in the group
SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of
singular spectrum can be shown by adapting an argument of Jaksic-Last if the
potential contains random Dirac peaks with absolutely continuous distribution.
