This letter presents a low-noise integrated potentiostat for affinity-free molecular detection in applications for personalized medicine. The affinity-free sensing technique uses a digital classifier to identify molecules through unique vibrational signatures. The sensing mechanism relies on coherent interference of electron wave functions at the interface between a nanoscale working electrode and a liquid electrolyte. Coherence at the sensing interface is enabled by low-noise feedback, which reduces the effective temperature of the electrons. The described three-channel potentiostat IC uses chopping and correlated double sampling to achieve an input-referred voltage noise of 12 nV/rt-Hz at 30 Hz and a current resolution of 1.8 pA_rms with 0.5-s averaging time. Each channel consumes 5 mW and occupies 0.41 mm² in 65-nm CMOS.