Grating-based X-ray dark-field imaging is a novel imaging modality with enormous technical progress during the last years. It enables the detection of microstructure impairment as in the healthy lung a strong dark-field signal is present due to the high number of air-tissue interfaces. Using the experience from setups for animal imaging, first studies with a human cadaver could be performed recently. Subsequently, the first dark-field scanner for in-vivo chest imaging of humans was developed. In the current study, the optimal tube voltage for dark-field radiography of the thorax in this setup was examined using an anthropomorphic chest phantom. Tube voltages of 50-125 kVp were used while maintaining a constant dose-area-product. The resulting dark-field and attenuation radiographs were evaluated in a reader study as well as objectively in terms of contrast-to-noise ratio and signal strength. We found that the optimum tube voltage for dark-field imaging is 70 kVp as here the most favorable combination of image quality, signal strength, and sharpness is present. At this voltage, a high image quality was perceived in the reader study also for attenuation radiographs, which should be sufficient for routine imaging. The results of this study are fundamental for upcoming patient studies with living humans.