We report on the first experimental demonstration of Compton imaging of gamma-rays with a single coaxial high-purity germanium (HPGe) detector. This imaging capability is realized by two-dimensional segmentation of the outside contact in combination with digital pulse-shape analysis, which enables to image gamma-rays in 4π without employing a collimator. We are able to demonstrate the ability to image the 662 keV gamma-ray from a 137Cs source with preliminary event selection, with an angular resolution of 5° and a relative efficiency of 0.3%. This efficiency expresses the fraction of gamma-rays that can be imaged, out of the total gamma-ray flux which is emitted into the solid angle of the detector. In addition to the 4π imaging capability, such a system is characterized by its excellent energy resolution and can be implemented in any size possible for Ge detectors to achieve high efficiency.