Due to the shortage of COVID-19 viral testing kits, radiology imaging is used to complement the screening process. Deep learning based methods are promising in automatically detecting COVID-19 disease in chest x-ray images. 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 the model on the newly collected COVID-19 chest x-ray dataset, often at a much smaller scale. However, simple fine-tuning may lead to poor performance for the CNN model due to two issues, firstly the large domain shift present in chest x-ray datasets and secondly the relatively 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 designed to align the data distributions across different domains in the general domain space and also in the 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.