Swarm Intelligence (SI) is a biological phenomenon in which groups of organisms amplify their combined brainpower by forming real-time systems. It has been studied for decades in fish schools, bird flocks, and bee swarms. Recent advances in networking and AI technologies have enabled distributed human groups to form closed-loop systems modeled after natural swarms. The process is referred to as Artificial Swarm Intelligence (ASI) and has been shown to significantly amplify group performance. The present research applies ASI technology to the field of medicine, exploring if small groups of networked radiologists can improve their diagnostic accuracy when reviewing chest X-rays for the presence of pneumonia. Performance data was collected for individual radiologists generating diagnoses alone, as well as for small groups of radiologists working together to generate diagnoses as a real-time ASI system. Diagnoses were also collected from a state-of-the-art deep learning system (CheXNet) developed at Stanford University. Results showed that small groups of networked radiologists, when working as a real-time ASI system, were significantly more accurate than the individual radiologists on their own, reducing diagnostic errors by 33%. Results also showed that small groups of networked radiologists, when working as an ASI system, were significantly more accurate (22%) than a state-of-the-art deep learning system (CheXNet).