We report both sub-diffraction-limited quantum metrology and quantum enhanced spatial resolution for the first time in a biological context. Nanoparticles are tracked with quantum correlated light as they diffuse through an extended region of a living cell in a quantum enhanced photonic force microscope. This allows spatial structure within the cell to be mapped at length scales down to 10 nm. Control experiments in water show a 14% resolution enhancement compared to experiments with coherent light. Our results confirm the longstanding prediction that quantum correlated light can enhance spatial resolution at the nanoscale and in biology. Combined with state-of-the-art quantum light sources, this technique provides a path towards an order of magnitude improvement in resolution over similar classical imaging techniques.