Context : KQ Vel is a peculiar A0p star with a strong surface magnetic field of about 7.5 kG . It has a slow rotational period of nearly 8 years . Bailey et al . ( 2015 ) detected a binary companion of uncertain nature , and suggested it could be a neutron star or a black hole . Aims : We analyze X-ray data obtained by the Chandra telescope to ascertain information about the stellar magnetic field and/or interaction between the star and its companion . Methods : We confirm previous X-ray detections of KQ Vel with a relatively large X-ray luminosity of 2 \times 10 ^ { 30 } erg s ^ { -1 } . X-ray spectra suggest the presence of hot gas at > 20 MK and , possibly , of a non-thermal component . X-ray light curves are variable , but better quality data are needed to determine periodicity if any . Results : We interpret X-ray spectra as a combination of two components : the non-thermal emission arising from the aurora on the A0p star and the hot thermal plasma filling the extended shell surrounding the “ propelling ” neutron star . Conclusions : We explore various alternatives , but a hybrid model involving the stellar magnetosphere along with a hot shell around the propelling neutron star seems most plausible.We speculate that KQ Vel was originally a triple system , and the Ap star is a merger product . We conclude that KQ Vel is an intermediate-mass binary consisting of a strongly magnetic main sequence star and a neutron star .