The recent discovery by LIGO/Virgo of a merging binary having a $\sim 23 M_\odot$ black hole and a $\sim 2.6 M_\odot$ compact companion has triggered a debate regarding the nature of the secondary, which falls into the so-called mass gap. Here we explore some consequences of the assumption that the secondary was a neutron star (NS). We show with concrete examples of heretofore viable equations of state (EOSs) that rapid uniform rotation may neither be necessary for some EOSs nor sufficient for others to explain the presence of a NS. Absolute upper limits for the maximum mass of a spherical NS derived from GW170817 already suggest that this unknown compact companion might be a slowly or even a nonrotating NS. However several soft NS EOSs favored by GW170817 with maximum spherical masses $\lesssim 2.1 M_\odot$ cannot be invoked to explain this object, even allowing for maximum uniform rotation. By contrast, sufficiently stiff EOSs that yield $2.6 M_\odot$ NSs which are slowly rotating or, in some cases, nonrotating, and are compatible with GW170817 and the results of NICER, can account for the black hole companion.