  Context. The eclipsing binary GU Mon is located in the star-forming cluster
Dolidze 25, which has the lowest metallicity measured in a Milky Way young
cluster. Aims. GU Mon has been identified as a short-period eclipsing binary
with two early B-type components. We set out to derive its orbital and stellar
parameters. Methods. We present a comprehensive analysis, including B and V
light curves and 11 high-resolution spectra, to verify the orbital period and
determine parameters. We use the stellar atmosphere code FASTWIND to obtain
stellar parameters and create templates for cross-correlation. We obtain a
model to fit the light and radial-velocity curves using the Wilson-Devinney
code iteratively and simultaneously. Results. The two components of GU Mon are
identical stars of spectral type B1 V, with the same mass and temperature. The
lightcurves are typical of an EW-type binary. The spectroscopic and photometric
analyses agree on a period of 0.896640 +- 0.000007 d. We determine a mass of
9.0 +- 0.6 Msun for each component and temperatures of 28 000 +- 2 000 K. Both
values are consistent with the spectral type. The two stars are overfilling
their respective Roche lobes, sharing a common envelope, and therefore the
orbit is synchronised and circularised. Conclusions. The GU Mon system has a
fill-out factor above 0.8, containing two dwarf B-type stars on the main
sequence. The two stars are in a very advanced stage of interaction, with their
extreme physical similarity likely due to the common envelope. The expected
evolution of such a system will very probably lead to a merger while still on
the main sequence.
