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We present a novel algorithm that is able to generate deep synthetic COVID-19 pneumonia CT scan slices using a very small sample of positive training images in tandem with a larger number of normal images. This generative algorithm produces images of sufficient accuracy to enable a DNN classifier to achieve high classification accuracy using as few as 10 positive training slices (from 10 positive cases), which to the best of our knowledge is one order of magnitude fewer than the next closest published work at the time of writing. Deep learning with extremely small positive training volumes is a very difficult problem and has been an important topic during the COVID-19 pandemic, because for quite some time it was difficult to obtain large volumes of COVID-19-positive images for training. Algorithms that can learn to screen for diseases using few examples are an important area of research. Furthermore, algorithms to produce deep synthetic images with smaller data volumes have the added benefit of reducing the barriers of data sharing between healthcare institutions. We present the cycle-consistent segmentation-generative adversarial network (CCS-GAN). CCS-GAN combines style transfer with pulmonary segmentation and relevant transfer learning from negative images in order to create a larger volume of synthetic positive images for the purposes of improving diagnostic classification performance. The performance of a VGG-19 classifier plus CCS-GAN was trained using a small sample of positive image slices ranging from at most 50 down to as few as 10 COVID-19-positive CT scan images. CCS-GAN achieves high accuracy with few positive images and thereby greatly reduces the barrier of acquiring large training volumes in order to train a diagnostic classifier for COVID-19.