  We present a search for a new heavy charged vector boson $W^\prime$ decaying
to an electron-neutrino pair in $p\bar{p}$ collisions at a center-of-mass
energy of $1.96\unit{TeV}$. The data were collected with the CDF II detector
and correspond to an integrated luminosity of $5.3\unit{fb}^{-1}$. No
significant excess above the standard model expectation is observed and we set
upper limits on $\sigma\cdot{\cal B}(W^\prime\to e\nu)$. Assuming standard
model couplings to fermions and the neutrino from the $W^\prime$ boson decay to
be light, we exclude a $W^\prime$ boson with mass less than
$1.12\unit{TeV/}c^2$ at the $95\unit{%}$ confidence level.
