The discovery of an X-ray binary RX J0209.6-7427 in the outer wing of the SMC is reported from two archival ROSAT PSPC observations. The data show variability in the X-ray light curve with a timescale of ~40 days that probably is related to the binary orbital period of the system. A V=14 mag star in the X-ray error circle of the source is the likely optical counterpart. The optical spectrum of the star shows Hα emission with an equivalent width of -10.8±0.2 Å. The spectral type of the star is constrained as B0-B1.5IV-Ve and consistent with that of a Be star. RX J0209.6-7427 is therefore a Be-type X-ray binary. The mean X-ray luminosity of the source is derived to be ~1.0×1038 erg s-1 (for a distance of 60 kpc), which is comparable to luminosities derived for Be-type X-ray binaries in the body of the SMC. This makes RX J0209.6-7427 the first candidate Be-type X-ray binary discovered in the outer SMC wing that directly extends into the Magellanic Bridge. This finding is consistent with the existence of a young (~10-30 Myr) stellar population in the outer region of the SMC wing. Star formation due to an encounter of the SMC with the LMC and the Magellanic system with the Galaxy may explain this likely high-mass X-ray binary in an area far from the main body of the SMC.