Use of He gas mixtures at atmospheric pressure (instead of low-pressure hydrocarbon gases) will ease the construction and operation of large-scale parallel-plate RICH detectors with CsI photocathodes. Due to the low density of He gas the number of primary electrons created by minimum-ionizing particles is very small even at atmospheric pressure. Therefore the Cherenkov detector will be nearly blind to ionizing tracks. However, He alone is not a good counting gas; a suitable quenching component must be added for stable operation of the chamber at high gas gain. Five different quenching gases, CH4, C2H6, isobutane, CF4 and CO2 have been tested at a mixing ratio of 5%. The first three gas mixtures show very promising performance. The parallel-plate avalanche chamber (PPAC) can be operated up to gains almost-equal-to 5 x 10(5) without secondary avalanches. When the He gas mixture includes 5% of the quenching gas (38 Torr) the efficiency for minimum-ionizing particles is calculated to be < 20% using a Monte Carlo simulation based on measured gas-gain spectra. Experimental investigation shows that the ratio of the quantum efficiency of a CsI photocathode in an atmospheric-pressure He/i-C4H10 (95/5) gas mixture to that in low-pressure i-C4H10 gas is almost-equal-to 75% for PPAC operation. The effect of mechanical tolerance on uniformity of gas gain at various pressures is also discussed in detail, and He/i-C4H10 (95/5) has the least variation of gain with gap thickness of the mixtures tested.