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6D object pose estimation is a fundamental problem in computer vision. Convolutional Neural Networks (CNNs) have recently proven to be capable of predicting reliable 6D pose estimates even from monocular images. Nonetheless, CNNs are identified as being extremely data-driven, and acquiring adequate annotations is oftentimes very time-consuming and labor intensive. To overcome this shortcoming, we propose the idea of monocular 6D pose estimation by means of self-supervised learning, removing the need for real annotations. After training our proposed network fully supervised with synthetic RGB data, we leverage recent advances in neural rendering to further self-supervise the model on unannotated real RGB-D data, seeking for a visually and geometrically optimal alignment. Extensive evaluations demonstrate that our proposed self-supervision is able to significantly enhance the model's original performance, outperforming all other methods relying on synthetic data or employing elaborate techniques from the domain adaptation realm.