  Using data from the E791 fixed-target hadroproduction experiment at Fermilab
we have studied the Cabibbo-favored but phase-space suppressed decay, $D^0 \to
K^- K^- K^+ \pi^+$. We find the decay rate for this mode to be $(0.54 \pm 0.16
\pm 0.08) \times 10^{-2}$ times that for the normalization mode $D^0 \to K^-
\pi^- \pi^+ \pi^+$. We observe a clear signal for $D^0 \to \phi K^- \pi^+$
which is consistent with producing $0.7 \pm 0.3$ of the $D^0 \to K^- K^- K^+
\pi^+$ signal. In the context of simple models, we use our measurements to
estimate the importance of decay amplitudes that produce extra quark-antiquark
pairs from the vacuum relative to those that do not.
