Lensless microscopes are simple, portable, and cost effective compared with the sophisticated microscopes of today that require high-end objectives, lenses, and filters. We demonstrate a lensless on-chip phase microscope based on the holographic principle to image 3D nanometric depth information from transparent and weakly scattering biological samples. We characterize the microscope using standard quantitative phase resolution target (PRT) charts with feature depths from 50 to 350 nm and report a signal-to-noise ratio value of 23 dB. Further, we apply a gradient descent-based constrained optimization approach for phase retrieval to eliminate the twin image and noise from the hologram. The device, operating as an inline holographic microscope, can perform quantitative phase imaging with nanometric depth sensitivity for a field of view of 29.4  mm² using an LED-based light source butt-coupled to an optical fiber cable.