  We have used the Australia Telescope Compact Array (ATCA) to search for
emission from the $4_{-1} \rightarrow 3_{0}E$ transition of methanol (36.2 GHz)
towards the center of the nearby starburst galaxy NGC253. Two regions of
emission were detected, offset from the nucleus along the same position angle
as the inner spiral arms. The emission is largely unresolved on a scale of 5
arcsec, has a full-width half maximum (FWHM) line width of < 30 km s$^{-1}$,
and an isotropic luminosity orders of magnitude larger than that observed in
any Galactic star formation regions. These characteristics suggest that the
36.2 GHz methanol emission is most likely a maser, although observations with
higher angular and spectral resolution are required to confirm this. If it is a
maser this represents the first detection of a class I methanol maser outside
the Milky Way. The 36.2 GHz methanol emission in NGC253 has more than an order
of magnitude higher isotropic luminosity than the widespread emission recently
detected towards the center of the Milky Way. If emission from this transition
scales with nuclear star formation rate then it may be detectable in the
central regions of many starburst galaxies. Detection of methanol emission in
ultra-luminous infra-red galaxies (ULIRGs) would open up a new tool for testing
for variations in fundamental constants (in particular the proton-to-electron
mass ratio) on cosmological scales.
