We adapted an existing, spaceflight-proven, robust "electronic nose" (E-Nose) that uses an array of electrical resistivity-based nanosensors mimicking aspects of mammalian olfaction to conduct on-site, rapid screening for COVID-19 infection by measuring the pattern of sensor responses to volatile organic compounds (VOCs) in exhaled human breath. We built and tested multiple copies of a hand-held prototype E-Nose sensor system, composed of 64 chemically sensitive nanomaterial sensing elements tailored to COVID-19 VOC detection; data acquisition electronics; a smart tablet with software (App) for sensor control, data acquisition and display; and a sampling fixture to capture exhaled breath samples and deliver them to the sensor array inside the E-Nose. The sensing elements detect the combination of VOCs typical in breath at parts-per-billion (ppb) levels, with repeatability of 0.02% and reproducibility of 1.2%; the measurement electronics in the E-Nose provide measurement accuracy and signal-to-noise ratios comparable to benchtop instrumentation. Preliminary clinical testing at Stanford Medicine with 63 participants, their COVID-19-positive or COVID-19-negative status determined by concomitant RT-PCR, discriminated between these two categories of human breath with a 79% correct identification rate using "leave-one-out" training-and-analysis methods. Analyzing the E-Nose response in conjunction with body temperature and other non-invasive symptom screening using advanced machine learning methods, with a much larger database of responses from a wider swath of the population, is expected to provide more accurate on-the-spot answers. Additional clinical testing, design refinement, and a mass manufacturing approach are the main steps toward deploying this technology to rapidly screen for active infection in clinics and hospitals, public and commercial venues, or at home.