We report the discovery of LXP169, a new high-mass X-ray binary (XRB) in the LMC. The optical counterpart has been identified and appears to exhibit an eclipsing light curve. We performed follow-up observations to clarify the eclipsing nature of the system. Energy spectra and time series were extracted from two XMM-Newton observations to search for pulsations, characterise the spectrum, and measure spectral and timing changes. Long-term X-ray variability was studied using archival ROSAT data. The XMM positions were used to identify the optical counterpart. We obtained UV to NIR photometry to characterise the companion, along with its 4000 d long I-band light curve. We observed LXP169 with Swift at two predicted eclipse times. We found a spin period of 168.8 s that did not change between two XMM observations. The X-ray spectrum, well characterised by a power law, was harder when the source was brighter. The X-ray flux of LXP169 is found to be variable by a factor of at least 10. The counterpart is highly variable on short and long timescales, and its photometry is that of an early-type star with a NIR excess. This classifies the source as a BeXRB pulsar. We observed a transit in the UV, thereby confirming that the companion star itself is eclipsed. We give an ephemeris for the transit of MJD 56203.877 + N*24.329. We propose and discuss the scenario where the matter captured from the companions equatorial disc creates an extended region of high density around the neutron star (NS), which partially eclipses the companion as the NS transits in front of it. This is most likely the first time the compact object in an XRB is observed to eclipse its companion star. LXP169 would be the first eclipsing BeXRB, and a wealth of important information might be gained from additional observations, such as a measure of the possible Be disc/orbital plane misalignment, or the mass of the NS.
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