Perhaps the greatest impediment to acquiring high-quality magnetoencephalography (MEG) recordings is the ubiquitous ambient magnetic field noise. We have designed and built a whole-head MEG system using a helmet-like superconducting imaging surface (SIS) surrounding the array of superconducting quantum interference device (SQUID) magnetometers used to measure the MEG signal. We previously demonstrated that the SIS passively shields the SQUID array from ambient magnetic field noise, independent of frequency, by 25-60 dB depending on sensor location. SQUID 'reference sensors' located on the outside of the SIS helmet measure ambient magnetic fields in very close proximity to the MEG magnetometers while being nearly perfectly shielded from all sources in the brain. The fact that the reference sensors measure no brain signal yet are located in close proximity to the MEG sensors enables very accurate estimation and subtraction of the ambient field noise contribution to the MEG sensors using an adaptive algorithm. We have demonstrated total ambient noise reduction factors in excess of 10(6) (> 120 dB). The residual noise for most MEG SQUID channels is at or near the intrinsic SQUID noise floor, typically 2-3 fT Hz-1/2. We are recording MEG signals with greater signal-to-noise than equivalent EEG measurements.