We report on magnetic field measurements made in the innermost coma of 67P/Churyumov-Gerasimenko in its low activity state. Quasi-coherent, large-amplitude ($delta B/B sim 1$), compressional magnetic field oscillations at $sim$ 40 mHz dominate the immediate plasma environment of the nucleus. This differs from previously studied comet-interaction regions where waves at the cometary ion gyro-frequencies are the main feature. Thus classical pick-up ion driven instabilities are unable to explain the observations. We propose a cross-field current instability associated with newborn cometary ion currents as a possible source mechanism.