  We report the detection of millihertz quasi-periodic oscillations
($\mathrm{mHz}$ QPOs) from the low-mass X-ray binary XTE J1701$-$462. The
discovery came from a search of the legacy data set of the Rossi X-ray Timing
Explorer, in order to detect the periodic signals in all observations of
sources exhibiting thermonuclear bursts. We found that $47$ out of $860$
observations of XTE J1701$-$462; covering the 2006-7 outburst exhibits signals
with a significance above the detection threshold, which was determined
separately for each observation via a Monte Carlo approach. We chose the four
strongest candidates, each with maximum power exceeding $4\sigma$ of the
simulated wavelet noise power distribution, to demonstrate the properties of
the QPOs. The frequencies of the signals in the four observations are $\sim
3.5\;\text{to}\;5.6\; \mathrm{mHz}$, and the fractional R.M.S. amplitudes vary
between $0.74 \pm 0.05\,\%$ and $3.54 \pm 0.04\,\%$. Although previously
reported signals in other sources typically disappear immediately before a
burst, we do not observe this behaviour in XTE J1701$-$462. Instead, we found
that the QPOs and bursts occurred in separate accretion regimes. When the
persistent luminosity dropped near the end of the outburst, the source showed
bursts and no QPOs were detected, which is the behaviour predicted by theory
for the transition from stable to unstable burning. On the basis of this new
detection, we reassess the cases for identifying these $\mathrm{mHz}$ QPOs in
this and other sources as arising from marginally stable burning.
