FRB 180916.J0158+65 is one of the nearest, periodically repeating, and actively bursting fast radio bursts (FRBs) that has been localized to the outskirts of a spiral galaxy. In this work we study the FRB with the hard X-ray 14-195keV data from the Burst Alert Telescope (BAT) on board The Neil Gehrels Swift Observatory. BAT uses coded mask technology giving a localization of 5{sigma} confidence level in any of the observations. We could estimate a 5{sigma} upper limit on the 14-195keV flux, which ranged between 4.5x10^-10^-7.6x10^-9^erg/cm2/s. At the source distance this relates to a 5{sigma} upper limit on a luminosity of 5.08x10^44^-8.5x10^45^erg/s. With this estimate, we could rule out any persistent X-ray emission at the source location for these snapshots of BAT observations.