  We study direct CP violation in the hadronic decay $B^{\pm} \to
\rho^{0}\pi^{\pm}$, including the effect of $\rho - \omega$ mixing. We find
that the CP violating asymmetry is strongly dependent on the CKM matrix
elements, especially the Wolfenstein parameter $\eta$. For fixed $N_{c}$ (the
effective parameter associated with factorization), the CP violating asymmetry,
$a$, has a maximum of order $30%-50%$ when the invariant mass of the
$\pi^{+}\pi^{-}$ pair is in the vicinity of the $\omega$ resonance. The
sensitivity of the asymmetry, $a$, to $N_{c}$ is small. Moreover, if $N_{c}$ is
constrained using the latest experimental branching ratios from the CLEO
collaboration, we find that the sign of $\sin \delta$ is always positive. Thus,
a measurement of direct CP violation in $B^{\pm} \to \rho^{0}\pi^{\pm}$ would
remove the mod$(\pi)$ ambiguity in ${\rm arg}[ -
\frac{V_{td}V_{tb}^{\star}}{V_{ud}V_{ub}^{\star}}]$.
