  We report the discovery of an eclipsing binary system with mass-ratio q
$\sim$ 0.07. After identifying a periodic photometric signal received by WASP,
we obtained CORALIE spectroscopic radial velocities and follow-up light curves
with the Euler and TRAPPIST telescopes. From a joint fit of these data we
determine that EBLM J0555-57 consists of a sun-like primary star that is
eclipsed by a low-mass companion, on a weakly eccentric 7.8-day orbit. Using a
mass estimate for the primary star derived from stellar models, we determine a
companion mass of $85 \pm 4 M_{\rm Jup}$ ($0.081M_{\odot}$) and a radius of
$0.84^{+0.14}_{-0.04} R_{\rm Jup}$ ($0.084 R_{\odot}$) that is comparable to
that of Saturn. EBLM J0555-57Ab has a surface gravity $\log g_\mathrm{2} =
5.50^{+0.03}_{-0.13}$ and is one of the densest non-stellar-remnant objects
currently known. These measurements are consistent with models of low-mass
stars.
