An analysis of airplane accidents reveals that pilots sometimes purely fail to react to critical auditory alerts. This inability of an auditory stimulus to reach consciousness has been coined under the term of inattentional deafness. Recent data from literature tends to show that tasks involving high cognitive load consume most of the attentional capacities, leaving little or none remaining for processing any unexpected information. In addition, there is a growing body of evidence for a shared attentional capacity between vision and hearing. In this context, the abundant information in modern cockpits is likely to produce inattentional deafness. We investigated this hypothesis by combining electroencephalographic (EEG) measurements with an ecological aviation task performed under contextual variation of the cognitive load (high or low), including an alarm detection task. Two different audio tones were played: standard tones and deviant tones. Participants were instructed to ignore standard tones and to report deviant tones using a response pad. More than 31% of the deviant tones were not detected in the high load condition. Analysis of the EEG measurements showed a drastic diminution of the auditory P300 amplitude concomitant with this behavioral effect, whereas the N100 component was not affected. We suggest that these behavioral and electrophysiological results provide new insights on explaining the trend of pilots' failure to react to critical auditory information. Relevant applications concern prevention of alarms omission, mental workload measurements and enhanced warning designs.