  We report a new precision measurement of the dc Stark shift of the
$6s\hspace{1mm} ^2S_{1/2} \rightarrow 7s\hspace{1mm}^2S_{1/2}$ transition in
atomic cesium-133. Our result is 0.72246 (29)
$\textrm{Hz}(\textrm{V}/\textrm{cm})^{-2}$. This result differs from a previous
measurement of the Stark shift by $\sim$0.5\%. We use this value to recalculate
the magnitude of the reduced dipole matrix elements $\langle7s
||r||7p_{j}\rangle$, as well as the vector transition polarizability for the
$6s \rightarrow 7s$ transition, $\tilde{\beta} = 27.043 \: (36) \ a_0^3$. This
determination helps resolve a critical discrepancy between two techniques for
determining the vector polarizability.
