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We report the discovery of a very young high-mass X-ray binary (HMXB) system associated with the supernova remnant (SNR) MCSNR J0513-6724 in the Large Magellanic Cloud (LMC), using XMM–Newton X-ray observations. The HMXB is located at the geometrical centre of extended soft X-ray emission, which we confirm as an SNR. The HMXB spectrum is consistent with an absorbed power law with spectral index ∼1.6 and a luminosity of 7 × 1033 erg s−1 (0.2–12 keV). Tentative X-ray pulsations are observed with a periodicity of 4.4 s and the OGLE I -band light curve of the optical counterpart from more than 17.5 yr reveals a period of 2.2324 ± 0.0003 d, which we interpret as the orbital period of the binary system. The X-ray spectrum of the SNR is consistent with non-equilibrium shock models as expected for young/less evolved SNRs. From the derived ionization time-scale we estimate the age of the SNR to be <6 kyr. The association of the HMXB with the SNR makes it the youngest HMXB, in the earliest evolutionary stage known to date. An HMXB as young as this can switch on as an accreting pulsar only when the spin period has reached a critical value. Under this assumption, we obtain an upper limit to the magnetic field of <5 × 1011 G. This implies several interesting possibilities including magnetic field burial, possibly by an episode of post-supernova hyper-critical accretion. Since these fields are expected to diffuse out on a time-scale of 103–104 yr, the discovery of a very young HMXB can provide us the unique opportunity to observe the evolution of the observable magnetic field for the first time in X-ray binaries. [ABSTRACT FROM AUTHOR]