Chemiresistive ammonia gas sensors with a low limit of detection of 0.15 ppm and moisture-independent characteristics based on p-type copper iodide (CuI) semiconductor films have been developed. CuI films were deposited on glass and polyethylene terephthalate (PET) substrates using a Successive Ionic Layer Adsorption and Reaction method to fabricate CuI/glass and CuI/PET gas sensors, respectively. They have a nanoscale morphology, an excess iodine and sulfur impurity content, a zinc blende γ-CuI crystal structure with a grain size of ~34 nm and an optical band gap of about 2.95 eV. The high selective sensitivity of both sensors to NH₃ is explained by the formation of the [Cu(NH₃)₂]⁺ complex. At 5 °C, the responses to 3 ppm ammonia in air in terms of the relative resistance change were 24.5 for the CuI/glass gas sensor and 28 for the CuI/PET gas sensor, with short response times of 50 s to 210 s and recovery times of 10–70 s. The sensors have a fast response–recovery and their performance was well maintained after long-term stability testing for 45 days. After 1000 repeated bends of the flexible CuI/PET gas sensor in different directions, with bending angles up to 180° and curvature radii up to 0.25 cm, the response changes were only 3%.