In stars, the fusion of ²²Ne and ⁴He may produce either ²⁵Mg, with the emission of a neutron, or ²⁶Mg and a γ ray. At high temperature, the (α, n) channel dominates, while at low temperature, it is energetically hampered. The rate of its competitor, the ²²Ne(α,γ)²⁶Mg reaction, and, hence, the minimum temperature for the (α, 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 ²⁶Mg). The data reported here have been obtained using high intensity ⁴He⁺ beam from the INFN LUNA 400 kV underground accelerator, a windowless, recirculating, 99.9% isotopically enriched ²²Ne gas target, and a 4π bismuth germanate summing γ-ray detector. The ultra-low background rate of less than 0.5 counts/day was determined using 63 days of no-beam data and 7 days of ⁴He⁺ beam on an inert argon target. The new high-sensitivity setup allowed to determine the first direct upper limit of 4.0×10^{- 11} eV (at 90% confidence level) for the resonance strength. Finally, the sensitivity of this setup paves the way to study further ²²Ne(α,γ)²⁶Mg resonances at higher energy.