Carrier-envelope phase stabilization has opened an avenue towards achieving frequency metrology with unprecedented precision and optical pulse generation on the previously inaccessible attosecond timescale. Recently, sub-100-as pulsegeneration has been demonstrated, approaching the timescale of the fastest transients in atomic physics. However, further progress in attophysics appears to be limited by the performance of the traditional feedback approach used for carrier-envelope phase stabilization. Here, we demonstrate a conceptually different self-referenced feed-forward approach to phase stabilization. This approach requires no complicated locking electronics, does not compromise laser performance, and is demonstrated with 12-as residual timing jitter, which is below the atomic unit of time. This surpasses the precision of previous methods by more than a factor of five and has potential for resolving even the fastest transients in atomic or molecular physics. Such shot-noise-limited comb synthesis may also simplify progress in current research in frequency metrology.