  Context. Mercury-manganese (HgMn) stars are a class of slowly rotating
chemically peculiar main-sequence late B-type stars. More than two-thirds of
the HgMn stars are known to belong to spectroscopic binaries.
  Aims. By determining orbital solutions for binary HgMn stars, we will be able
to obtain the masses for both components and the distance to the system.
Consequently, we can establish the position of both components in the
Hertzsprung-Russell diagram and confront the chemical peculiarities of the HgMn
stars with their age and evolutionary history.
  Methods. We initiated a program to identify interferometric binaries in a
sample of HgMn stars, using the PIONIER near-infrared interferometer at the
VLTI on Cerro Paranal, Chile. For the detected systems, we intend to obtain
full orbital solutions in conjunction with spectroscopic data.
  Results. The data obtained for the SB2 system 41 Eridani allowed the
determination of the orbital elements with a period of just five days and a
semi-major axis of under 2 mas. Including published radial velocity
measurements, we derived almost identical masses of 3.17 +/- 0.07 M_Sun for the
primary and 3.07 +/- 0.07 M_Sun for the secondary. The measured magnitude
difference is less than 0.1 mag. The orbital parallax is 18.05 +/- 0.17 mas,
which is in good agreement with the Hipparcos trigonometric parallax of 18.33
+/- 0.15 mas. The stellar diameters are resolved as well at 0.39 +/- 0.03 mas.
The spin rate is synchronized with the orbital rate.
