In this paper we discuss some preliminary results on using Widrow's Adaptive Noise Cancelling (ANC) algorithm to reduce the background noise present in a fighter pilot's speech. With a dominant noise source present and with the pilot wearing an oxygen facemask, we demonstrate that good (>10 dB) cancellation of the additive noise and little speech distortion can be achieved by having the reference microphone attached to the outside of the facemask and by updating the filter coefficients only during silence intervals.