The cardiothoracic ratio (CTR), a clinical metric of heart size in chest X-rays (CXRs), is a key indicator of cardiomegaly. Manual measurement of CTR is time-consuming and can be affected by human subjectivity, making it desirable to design computer-aided systems that assist clinicians in the diagnosis process. Automatic CTR estimation through chest organ segmentation, however, requires large amounts of pixel-level annotated data, which is often unavailable. To alleviate this problem, we propose an unsupervised domain adaptation framework based on adversarial networks. The framework learns domain invariant feature representations from openly available data sources to produce accurate chest organ segmentation for unlabeled datasets. Specifically, we propose a model that enforces our intuition that prediction masks should be domain independent. Hence, we introduce a discriminator that distinguishes segmentation predictions from ground truth masks. We evaluate our system's prediction based on the assessment of radiologists and demonstrate the clinical practicability for the diagnosis of cardiomegaly. We finally illustrate on the JSRT dataset that the semi-supervised performance of our model is also very promising.