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A new technique is presented for high-pressure gaseous radiation detectors leading to pulse amplitudes at least one order of magnitude larger than in ionization-chamber-based gamma-ray detectors. The technique uses room-temperature pure Xe or Xe-based gaseous mixtures at pressures of about 5-20 bar (or higher) to detect ionizing radiation in a multigrid high-pressure gas proportional scintillation counter (MGHP-GPSC) with a CsI deposit as the photocathode in direct contact with the gas, with no optical windows. The detector relies on secondary scintillation as the amplification stage followed by photoelectron production in a CsI photocathode layer. Experimental results are presented for a small prototype filled with pure Xe up to 5 bar, showing that the principle of operation of the detector works. The maximum detector gain obtained so far is about 10.