  We report the first detection of deuterated water (HDO) toward an
extragalactic hot core. The HDO 2$_{11}$-2$_{12}$ line has been detected toward
hot cores N105-2A and 2B in the N105 star-forming region in the low-metallicity
Large Magellanic Cloud (LMC) dwarf galaxy with the Atacama Large
Millimeter/submillimeter Array (ALMA). We have compared the HDO line luminosity
($L_{\rm HDO}$) measured toward the LMC hot cores to those observed toward a
sample of seventeen Galactic hot cores covering three orders of magnitude in
$L_{\rm HDO}$, four orders of magnitude in bolometric luminosity ($L_{\rm
bol}$), and a wide range of Galactocentric distances (thus metallicities). The
observed values of $L_{\rm HDO}$ for the LMC hot cores fit very well into the
$L_{\rm HDO}$ trends with $L_{\rm bol}$ and metallicity observed toward the
Galactic hot cores. We have found that $L_{\rm HDO}$ seems to be largely
dependent on the source luminosity, but metallicity also plays a role. We
provide a rough estimate of the H$_2$O column density and abundance ranges
toward the LMC hot cores by assuming that HDO/H$_2$O toward the LMC hot cores
is the same as that observed in the Milky Way; the estimated ranges are
systematically lower than Galactic values. The spatial distribution and
velocity structure of the HDO emission in N105-2A is consistent with HDO being
the product of the low-temperature dust grain chemistry. Our results are in
agreement with the astrochemical model predictions that HDO is abundant
regardless of the extragalactic environment and should be detectable with ALMA
in external galaxies.
