  A possible mechanism to explain the origin of the light $p$-nuclei in the
Galaxy is the nucleosynthesis in the proton-rich neutrino-driven wind ejecta of
core-collapse supernovae via the $\nu p$-process. However this production
scenario is very sensitive to the underlying supernova dynamics and the nuclear
physics input. As far as the nuclear uncertainties are concerned, the breakout
from the $pp$-chains via the $^7$Be($\alpha,\gamma$)$^{11}$C reaction has been
identified as an important link which can influence the nuclear flow and
therefore the efficiency of the $\nu p$-process. However its reaction rate is
poorly known over the relevant temperature range, T = 1.5-3 GK. We report on
the first direct measurement of two resonances of the
$^7$Be($\alpha,\gamma$)$^{11}$C reaction with previously unknown strengths
using an intense radioactive $^7$Be beam from the ISAC facility and the DRAGON
recoil separator in inverse kinematics. We have decreased the
$^7$Be($\alpha,\gamma$)$^{11}$C reaction rate uncertainty to $\sim$ 9.4-10.7%
over the relevant temperature region.
