  In stars, the fusion of $^{22}$Ne and $^4$He may produce either $^{25}$Mg,
with the emission of a neutron, or $^{26}$Mg and a $\gamma$ ray. At high
temperature, the ($\alpha,n$) channel dominates, while at low temperature, it
is energetically hampered. The rate of its competitor, the
$^{22}$Ne($\alpha$,$\gamma$)$^{26}$Mg reaction, and, hence, the minimum
temperature for the ($\alpha,n$) dominance, are controlled by many nuclear
resonances. The strengths of these resonances have hitherto been studied only
indirectly. The present work aims to directly measure the total strength of the
resonance at $E$_{r}$\,=\,$334$\,$keV (corresponding to
$E$_{x}$\,=\,$10949$\,$keV in $^{26}$Mg). The data reported here have been
obtained using high intensity $^4$He$^+$ beam from the INFN LUNA 400 kV
underground accelerator, a windowless, recirculating, 99.9% isotopically
enriched $^{22}$Ne gas target, and a 4$\pi$ bismuth germanate summing
$\gamma$-ray detector. The ultra-low background rate of less than 0.5
counts/day was determined using 67 days of no-beam data and 7 days of
$^4$He$^+$ beam on an inert argon target. The new high-sensitivity setup
allowed to determine the first direct upper limit of 4.0$\,\times\,$10$^{-11}$
eV (at 90% confidence level) for the resonance strength. Finally, the
sensitivity of this setup paves the way to study further
$^{22}$Ne($\alpha$,$\gamma$)$^{26}$Mg resonances at higher energy.
