  We present a novel measurement of the pairwise peculiar velocity distribution
function of galaxies on scales $r<3200$ \kmsec in the Las Campanas Redshift
Survey. The distribution is well described by a scale-independent exponential
with a width $\tau$ where $\sig =\sqrt{2}\tau=363$ \kmsec. The signal is very
stable. Results from the Northern and Southern sets of slices agree within
$\pm13$ \kmsec and the fluctuations among the six individual survey slices vary
as $\pm44$ \kmsec. The distribution was determined using a Fourier-space
deconvolution of the redshift-space distortions in the correlation function.
This technique is insensitive to the effect of rich clusters in the survey and
recovers the entire distribution function rather than just its second moment.
Taken together with the large effective volume of the survey $6.0\times10^6
\Mpc^3$, we believe this to be a definitive result for $r$-band selected
galaxies with absolute magnitudes $-18.5 <M_r<-22.5$ and $z<0.2$.
