We present a lens-free optical tomographic microscope, which enables imaging a large volume of approximately 15 mm³ on a chip, with a spatial resolution of < 1 μm x < 1 μm x < 3 μm in x, y and z dimensions, respectively. In this lens-free tomography modality, the sample is placed directly on a digital sensor array with, e.g., less-than or equal to 4 mm distance to its active area. A partially coherent light source placed approximately 70 mm away from the sensor is employed to record lens-free in-line holograms of the sample from different viewing angles. At each illumination angle, multiple subpixel shifted holograms are also recorded, which are digitally processed using a pixel superresolution technique to create a single high-resolution hologram of each angular projection of the object. These superresolved holograms are digitally reconstructed for an angular range of ± 50°, which are then back-projected to compute tomograms of the sample. In order to minimize the artifacts due to limited angular range of tilted illumination, a dual-axis tomography scheme is adopted, where the light source is rotated along two orthogonal axes. Tomographic imaging performance is quantified using microbeads of different dimensions, as well as by imaging wild-type Caenorhabditis elegans. Probing a large volume with a decent 3D spatial resolution, this lens-free optical tomography platform on a chip could provide a powerful tool for high-throughput imaging applications in, e.g., cell and developmental biology.