Using lensfree holography we demonstrate optofluidic tomography on a chip. A partially coherent light source is utilized to illuminate the objects flowing within a microfluidic channel placed directly on a digital sensor array. The light source is rotated to record lensfree holograms of the objects at different viewing directions. By capturing multiple frames at each illumination angle, pixel super-resolution techniques are utilized to reconstruct high-resolution transmission images at each angle. Tomograms of flowing objects are then computed through filtered back-projection of these reconstructed lensfree images, thereby enabling optical sectioning on-a-chip. The proof-of-concept is demonstrated by lensfree tomographic imaging of C. elegans.