  We propose a chiral Pati-Salam theory based on the gauge group $SU(4)_C\times
SU(2)_L\times SU(2)_R$. The left-handed quarks and leptons are unified into a
fundamental representation of $SU(4)_C$, while right-handed quarks and leptons
have a separate treatment. The deviations measured in the rare semi-leptonic
decays $B\to D^{(*)} \tau\bar\nu$ are explained by a scalar leptoquark which
couples to right-handed fields and is contained in the $SU(4)_C\times SU(2)_R$
breaking scalar multiplet. The measured deviation of lepton flavor universality
in the rare decays $\bar B\to \bar K^{(*)}\ell^+\ell^-$, $\ell=\mu,e$ is
explained via the $SU(4)_C$ leptoquark gauge boson. The model predicts a new
sub-GeV scale sterile neutrino which participates in the anomaly and can be
searched for in upcoming neutrino experiments. The theory satisfies the current
most sensitive experimental constraints and its allowable parameter regions
will be probed as more precise measurements from the LHCb and Belle II
experiments become available.
