Context. According to our current understanding, a subclass of the upper main-sequence chemically peculiar stars, called mercurymanganese (HgMn), is non-magnetic. Nevertheless, chemical inhomogeneities were recently discovered on their surfaces. At the same time, no global magnetic fields stronger than 1-100 G are detected by systematic studies. Aims. The goals of our study are to search for a magnetic field in the HgMn binary system 66 Eri and to investigate chemical spots on the stellar surfaces of both components. Methods. Our analysis is based on high-quality spectropolarimetric time-series observations obtained during 10 consecutive nights with the HARPSpol instrument at the ESO 3.6-m telescope. To increase the sensitivity of the magnetic field search we employed a least-squares deconvolution (LSD). We used spectral disentangling to measure radial velocities and study the line profile variability. Chemical spot geometry was reconstructed using multi-line Doppler imaging. Results. We report a non-detection of magnetic field in 66 Eri, with error bars 10-24 G for the longitudinal field. Circular polarization profiles also do not indicate any signatures of complex surface magnetic fields. For a simple dipolar field configuration we estimated an upper limit of the polar field strength to be 60-70 G. For the HgMn component we found variability in spectral lines of Ti, Ba, Y, and Sr with the rotational period equal to the orbital one. The surface maps of these elements reconstructed with the Doppler imaging technique show a relative underabundance on the hemisphere facing the secondary component. The contrast of chemical inhomogeneities ranges from 0.4 for Ti to 0.8 for Ba.