We discuss the fabrication of gas-analytical multisensor arrays based on ZnO nanorods grown via a hydrothermal route directly on a multielectrode chip. The protocol to deposit the nanorods over the chip includes the primary formation of ZnO nano-clusters over the surface and secondly the oxide hydrothermal growth in a solution that facilitates the appearance of ZnO nanorods in the high aspect ratio which comprise a network. We have tested the proof-of-concept prototype of the ZnO nanorod network-based chip heated up to 400 °C versus three alcohol vapors, ethanol, isopropanol and butanol, at approx. 0.2–5 ppm concentrations when mixed with dry air. The results indicate that the developed chip is highly sensitive to these analytes with a detection limit down to the sub-ppm range. Due to the pristine differences in ZnO nanorod network density the chip yields a vector signal which enables the discrimination of various alcohols at a reasonable degree via processing by linear discriminant analysis even at a sub-ppm concentration range suitable for practical applications.