Context. Be/X-ray binaries, the most common class of high-mass X-ray binaries, are characterised by OBe companions, but they display a rich variety of X-ray behaviours. One of the most atypical systems is X0726−260, which also has the earliest optical counterpart among the whole Milky Way and Magellanic Cloud sample. Aims. We intend to improve the characterisation of its optical counterpart, LS 437, and to constrain the physical mechanisms responsible for the anomalous properties of X0726−260. Methods. We analysed high-quality high-resolution optical spectroscopy of LS 437 with the standard quantitative methodology to derive the stellar parameters. We also made use of archival X-ray monitoring. Results. We derived a moderate projected rotational velocity of v sin i ≍ 155 km s−1 and a spectral type O7.5 Ve (Teff = 36 000 K), which means that LS 437 is substantially earlier than any other Oe star in an X-ray binary. At this spectral type, the stellar wind likely contributes significantly to mass accretion, and the X-ray light curve is strongly suggestive of an orbitally modulated wind accretor. The source shows marked carbon depletion, whereas nitrogen is only slightly above solar abundance. Conclusions. LS 437 is one of the earliest Oe stars known in the Galaxy, alongside HD 155806. Long-term X-ray light curves of X0726−260 strengthen the identification of a persistent 34.5 d periodicity as the orbital period, demonstrating that the X-ray emission is orbitally modulated, and no X-ray outbursts have occurred over the past 30 years. Likewise, emission features in the optical spectrum indicate a remarkably stable circumstellar disk, with no sign of major structural changes over the past 40 years. All of these characteristics clearly set X0726−260 apart from typical Be/X-ray binaries.