  This paper presents a detailed analysis of the light and radial velocity
curves of the semi-detached eclipsing binary system OGLE-LMC-ECL-09937. The
system is composed of a hot, massive and luminous primary star of a late-O
spectral type, and a more evolved, but less massive and luminous secondary,
implying an Algol-type system that underwent a mass transfer episode. We derive
masses of 21.04 +/- 0.34 M_Sun and 7.61 +/- 0.09 M_Sun and radii of 9.93 +/-
0.06 R_Sun and 9.18 +/- 0.04 R_Sun, for the primary and the secondary
component, respectively, which make it the most massive known Algol-type system
with masses and radii of the components measured with <2% accuracy.
Consequently, the parameters of OGLE-LMC-ECL-09937 provide an important
contribution to the sparsely populated high-mass end of the stellar mass
distribution, and an interesting object for stellar evolution studies, being a
possible progenitor of a binary system composed of two neutron stars.
