Neural recording systems that interface with implanted microelectrodes are used extensively in experimental neuroscience and neural engineering research. Interface electronics that are needed to amplify, filter, and digitize signals from multichannel electrode arrays are a critical bottleneck to scaling such systems. This paper presents the design and testing of an electronic architecture for intracortical neural recording that drastically reduces the size per channel by rapidly multiplexing many electrodes to a single circuit. The architecture utilizes mixed-signal feedback to cancel electrode offsets, windowed integration sampling to reduce aliased high-frequency noise, and a successive approximation analog-to-digital converter with small capacitance and asynchronous control. Results are presented from a 180 nm CMOS integrated circuit prototype verified using in vivo experiments with a tungsten microwire array implanted in rodent cortex. The integrated circuit prototype achieves <0.004 mm2 area per channel, 7 µW power dissipation per channel, 5.6 µVrms input referred noise, 50 dB common mode rejection ratio, and generates 9-bit samples at 30 kHz per channel by multiplexing at 600 kHz. General considerations are discussed for rapid time domain multiplexing of high-impedance microelectrodes. Overall, this work describes a promising path forward for scaling neural recording systems to numbers of electrodes that are orders of magnitude larger.