  We present a new technique, `Tau Polarimetry', for measuring the longitudinal
beam polarization present in an $e^+e^-$ collider through the analysis of
$e^+e^-\rightarrow\tau^+\tau^-$ events. By exploiting the sensitivity of $\tau$
decay kinematics to the longitudinal polarization of the beams, we demonstrate
that the longitudinal polarization can be measured with a 3 per mil systematic
uncertainty at the interaction point using a technique that is independent of
spin and beam transport modeling. Using 424.2$\pm$1.8 fb$^{-1}$ of BABAR data
at $\sqrt{s}=10.58$ GeV, the average longitudinal polarization of the PEP-II
$e^+e^-$ collider has been measured to be $\langle P\rangle=0.0035 \pm
0.0024_{\textrm{stat}}\pm 0.0029_{\textrm{sys}}$. The systematic uncertainty
studies are described in detail, which can serve as a guide for future
applications of Tau Polarimetry. A proposed $e^-$ beam longitudinal
polarization upgrade to the SuperKEKB $e^+e^-$ collider would benefit from this
technique.
