Neutron stars are possible end products of massive star evolution (M ≥ 8 Msun). They are exotic astronomical objects observed with masses between 1.2 and 2.35 Msun and typically emitting at radio and X-ray wavelengths, especially when being young and rapidly rotating. As they age, their rotation slows down, their emission fades, and they become ‘quiet’, unless they are fuelled by mass transfer from a binary companion. Neutron stars not powered by accretion are difficult to detect and, therefore, very rarely observed. Here, we propose that the giant star in 56 UMa has a neutron star companion in a 46-yr orbit. Combining radial-velocity with HIPPARCOS and Gaia astrometric data, we derived its mass to be 1.31 Msun. Our claim is supported by the discovery of a cavity in the HI interstellar gas around the star, providing evidence of a supernova explosion. The heavy-element abundance profile of the giant bears imprints from the s-process and seemingly as well from the r-process of nucleosynthesis, making it the first known star with a combined rs-pattern at solar metallicity. Our finding opens an opportunity to explore evolutionary scenarios that could lead to such a system and to derive properties related to the progenitor of this supernova that exploded ~100 000 years ago only 170 pc away from Earth.