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Due to the shortage of COVID-19 viral testing kits and the long waiting time, radiology imaging is used to complement the screening process and triage patients into different risk levels. Deep learning based methods have taken an active role in automatically detecting COVID-19 disease in chest x-ray images, as witnessed in many recent works in early 2020. Most of these works first train a Convolutional Neural Network (CNN) on an existing large-scale chest x-ray image dataset and then fine-tune it with a COVID-19 dataset at a much smaller scale. However, direct transfer across datasets from different domains may lead to poor performance for CNN due to two issues, the large domain shift present in the biomedical imaging datasets and the extremely small scale of the COVID-19 chest x-ray dataset. In an attempt to address these two important issues, we formulate the problem of COVID-19 chest x-ray image classification in a semi-supervised open set domain adaptation setting and propose a novel domain adaptation method, Semi-supervised Open set Domain Adversarial network (SODA). SODA is able to align the data distributions across different domains in a general domain space and also in a common subspace of source and target data. In our experiments, SODA achieves a leading classification performance compared with recent state-of-the-art models in separating COVID-19 with common pneumonia. We also present initial results showing that SODA can produce better pathology localizations in the chest x-rays.