Electroencephalograph (EEG) recording systems offer a versatile, noninvasive window on the brain's spatio-temporal activity for many neuroscience and clinical applications. Our research aims at improving the spatial resolution and mobility of EEG recording by reducing the form factor, power drain and signal fanout of the EEG acquisition node in a scalable sensor array architecture. We present such a node integrated onto a dimesized circuit board that contains a sensor's complete signal processing front-end, including amplifier, filters, and analog-to-digital conversion. A daisy-chain configuration between boards with bit-serial output reduces the wiring needed. The circuit's low power consumption of 423 μW supports EEG systems with hundreds of electrodes to operate from small batteries for many hours. Coupling between the bit-serial output and the highly sensitive analog input due to dense integration of analog and digital functions on the circuit board results in a deterministic noise component in the output, larger than the intrinsic sensor and circuit noise. With software correction of this noise contribution, the system achieves an input-referred noise of 0.277 μVrms in the signal band of 1 to 100 Hz, comparable to the best medical-grade systems in use. A chain of seven nodes using EEG dry electrodes created in micro-electrical-mechanical system (MEMS) technology is demonstrated in a real-world setting.