X-ray tomography can provide structural information of whole cells in close to their native state. Radiation-induced damage, however, imposes a practical limit to image resolution, and as such, a choice between damage, image contrast, and image resolution must be made. New coherent diffractive imaging techniques, such Fresnel Coherent Diffractive Imaging (FCDI), allows quantitative phase information with exceptional dose efficiency, high contrast, and nano-scale resolution. Here we present three-dimensional quantitative images of a whole eukaryotic cell by FCDI at a spatial resolution below 70 nm with sufficient phase contrast to distinguish major cellular components. From our data, we estimate that the minimum dose required for a similar resolution is close to that predicted by the Rose criterion, considerably below accepted estimates of the maximum dose a frozen-hydrated cell can tolerate. Based on the dose efficiency, contrast, and resolution achieved, we expect this technique will find immediate applications in tomographic cellular characterisation.