Pervaporation is an energy-efficient alternative to conventional distillation for water/alcohol separations. In this work, a novel CHA zeolite membrane with an increased Si/Al ratio was synthesized in the absence of organic templates for the first time. Nanosized high-silica zeolite (SSZ-13) seeds were used for the secondary growth of the membrane. The separation performance of membranes in different alcohol–aqueous mixtures was measured. The effects of water content in the feed and the temperature on the separation performance using pervaporation and vapor permeation were also studied. The best membrane showed a water/ethanol separation factor above 100,000 and a total flux of 1.2 kg/(m2 h) at 348 K in a 10 wt.% water–ethanol mixed solution. A membrane with high performance and an increased Si/Al ratio is promising for the application of alcohol dehydration.