We propose to improve the spatial resolution of electroencephalography (EEG) using a differential recording methodology. Conventional EEG (CEEG) systems independently amplify and digitize the signal from each electrode. The Differential EEG (DEEG) approach amplifies the minute difference signal between neighboring electrodes which greatly eases the burden on the subsequent amplification and data conversion stages. A custom DEEG system was designed and fabricated in a 0.6 um CMOS process. The fabricated chip was built into a small prototype DEEG recording system used to measure alpha waves from the occipital lobe of a human subject. We show that the differential approach suffers from fewer artifacts in an eye open/closed determination task than a commercial CEEG system. Artifacts are mainly due to the signal level dependent noise and amplifier mismatch in the CEEG amplifiers. All of our experiments were run with a fixed 3 cm electrode spacing, however we expect to improve the resolution of EEG below 1 cm electrode spacing.