We experimentally illustrate a lensfree holographic imaging platform to perform on-chip cytometry. By controlling the spatial coherence of the illumination source, we record a 2D holographic diffraction pattern of each cell or micro-particle on a chip using a high resolution sensor array that has approximately 2 microm pixel size. The recorded holographic image is then processed by using a custom developed decision algorithm for matching the detected hologram texture to existing library images for on-chip characterization and counting of a heterogeneous solution of interest. The holographic diffraction signature of any microscopic object is significantly different from the classical diffraction pattern of the same object. It improves the signal to noise ratio and the signature uniformity of the cell patterns; and also exhibits much better sensitivity for on-chip imaging of weakly scattering phase objects such as small bacteria or cells. We verify significantly improved performance of this holographic on-chip cytometry approach by automatically characterizing heterogeneous solutions of red blood cells, yeast cells, E. coli and various sized micro-particles without the use of any lenses or microscope objectives. This lensless on-chip holography platform will especially be useful for point-of-care cytometry and diagnostics applications involving e.g., infectious diseases such as HIV or malaria.