  Based on the largest catalogs currently available, comprising 6090 contact
binaries (CBs) and 2167 open clusters, we determine the near-infrared $JHK_{\rm
s}$ CB period--luminosity (PL) relations, for the first time achieving the low
levels of intrinsic scatter that make these relations viable as competitive
distance calibrators. To firmly establish our distance calibration on the basis
of open cluster CBs, we require that (i) the CB of interest must be located
inside the core radius of its host cluster; (ii) the CB's proper motion must be
located within the $2\sigma$ distribution of that of its host open cluster; and
(iii) the CB's age, $t$, must be comparable to that of its host cluster, i.e.,
$\Delta \log (t\mbox{ yr}^{-1}) <0.3$. We thus select a calibration sample of
66 CBs with either open cluster distances or accurate space-based parallaxes.
The resulting near-infrared PL relations, for both late-type (i.e., W Ursae
Majoris-type) and---for the first time---early-type CBs, are as accurate as the
well-established $JHK_{\rm s}$ Cepheid PL relations, (characterized by
single-band statistical uncertainties of $\sigma < 0.10$ mag). We show that CBs
can be used as viable distance tracers, yielding distances with uncertainties
of better than 5\% for 90\% of the 6090 CBs in our full sample. By combining
the full $JHK_{\rm s}$ photometric data set, CBs can trace distances with an
accuracy, $\sigma=0.05 \mbox{ (statistical)} \pm0.03 \mbox{ (systematic)}$ mag.
The 102 CBs in the Large Magellanic Cloud are used to determine a distance
modulus to the galaxy of $(m-M_V)_0^{\rm LMC}=18.41\pm0.20$ mag.
