  We report the first extragalactic detection of the complex organic molecules
(COMs) dimethyl ether (CH$_3$OCH$_3$) and methyl formate (CH$_3$OCHO) with the
Atacama Large Millimeter/submillimeter Array (ALMA). These COMs together with
their parent species methanol (CH$_3$OH), were detected toward two 1.3 mm
continuum sources in the N 113 star-forming region in the low-metallicity Large
Magellanic Cloud (LMC). Rotational temperatures ($T_{\rm rot}\sim130$ K) and
total column densities ($N_{\rm rot}\sim10^{16}$ cm$^{-2}$) have been
calculated for each source based on multiple transitions of CH$_3$OH. We
present the ALMA molecular emission maps for COMs and measured abundances for
all detected species. The physical and chemical properties of two sources with
COMs detection, and the association with H$_2$O and OH maser emission indicate
that they are hot cores. The fractional abundances of COMs scaled by a factor
of 2.5 to account for the lower metallicity in the LMC are comparable to those
found at the lower end of the range in Galactic hot cores. Our results have
important implications for studies of organic chemistry at higher redshift.
