  We present CO(2-1), $^{13}$CO(2-1), CO(6-5), CO(7-6), and SO(6$_5-5_4$) line
observations made with the {\it IRAM 30 m} and {\it APEX} radiotelescopes and
the {\it Submillimeter Array} toward the highly collimated and extended
southwest lobe of the bipolar outflow {\it Ori-S6} located in the Orion South
region. We report, for all these lines, the detection of velocity asymmetries
about the flow axis, with velocity differences roughly on the order of 1 km
s$^{-1}$ over distances of about 5000 AU, 4 km s$^{-1}$ over distances of about
2000 AU, and close to the source of between 7 and 11 km s$^{-1}$ over smaller
scales of about 1000 AU. We interpret these velocity differences as a signature
of rotation but also discuss some alternatives which we recognize as unlikely
in view of the asymmetries' large downstream continuation. This rotation across
the {\it Ori-S6} outflow is observed out to (projected) distances beyond 2.5
$\times$ 10$^4$ AU from the flow's presumed origin. Comparison of our
large-scale and small-scale observations suggests the rotational velocity to
decline not faster than 1/R with distance R from the axis; in the innermost few
arcsecs an increase of rotational velocity with R is even indicated. The
magnetic field lines threading the inner rotating CO shell may well be anchored
in a disk of radius $\sim$ 50 AU; the field lines further out need a more
extended rotating base.
