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Intense X-ray free-electron lasers (XFELs) can rapidly excite matter, leaving it in inherently unstable states that decay on femtosecond timescales. As the relaxation occurs primarily via Auger emission, excited state observations are constrained by Auger decay. In situ measurement of this process is therefore crucial, yet it has thus far remained elusive at XFELs due to inherent timing and phase jitter, which can be orders of magnitude larger than the timescale of Auger decay. Here, we develop a new approach termed self-referenced attosecond streaking, based upon simultaneous measurements of streaked photo- and Auger electrons. Our technique enables sub-femtosecond resolution in spite of jitter. We exploit this method to make the first XFEL time-domain measurement of the Auger decay lifetime in atomic neon, and, by using a fully quantum-mechanical description, retrieve a lifetime of $2.2^{ + 0.2}_{ - 0.3}$ fs for the KLL decay channel. Importantly, our technique can be generalised to permit the extension of attosecond time-resolved experiments to all current and future FEL facilities.