  We present evidence of anisotropic galaxy assembly bias in the Baryon
Oscillation Spectroscopic Survey Data Release 12 galaxy sample at a level
exceeding $5\sigma$. We use measurements of the line-of-sight velocity
dispersion $\sigma_\star$ and stellar mass $M_\star$ to perform a simple split
into subsamples of galaxies. We show that the amplitude of the monopole and
quadrupole moments of the power spectrum depend differently on $\sigma_\star$
and $M_\star$, allowing us to split the galaxy sample into subsets with
matching monopoles but significantly different quadrupoles on all scales.
Combining data from the LOWZ and CMASS NGC galaxy samples, we find $>5\sigma$
evidence for anisotropic bias on scales $k<0.15\,h\,\rm{Mpc}^{-1}$. We also
examine splits using other observed properties. For galaxy samples split using
$M_\star$ and projected size $R_0$, we find no significant evidence of
anisotropic bias. Galaxy samples selected using additional properties exhibit
strongly varying degrees of anisotropic assembly bias, depending on which
combination of properties is used to split into subsets. This may explain why
previous searches for this effect using the Fundamental Plane found
inconsistent results. We conclude that any selection of a galaxy sample that
depends on $\sigma_\star$ can give biased and incorrect Redshift Space
Distortion measurements.
