The introduction of magnetic charge into Maxwells equations has led to an extensive search for magnetically charged particles (magnetic monopoles). A particle model developed by one of us (DF) adds an additional feature to Maxwells symmetric equations in that the stable magnetic monopole should have the same charge strength as the electron. We have not found any experiments in high-energy physics that have explicitly ruled out this possibility. However, the few experiments at colliders that had no magnetic field might have observed a signal for these 1e strength magnetic monopoles as an unexpected enhancement in the mu+mu- production rate. The absence of any such observation leads us to set a tentative lower mass limit for these unit charge magnetic monopoles at 4.5-5 GeV/c2. Using a MC generator for magnetic charge and tracking these events through a simplified model of the BELLE II detector, we have found that the central drift chamber of BELLE II has a remarkably high efficiency for triggering on magnetically charged tracks. We suggest that the BELLE II collaboration perform a specific search for stable magnetically charged particles having a field strength of 1e when they run for the first time with colliding beams in 2018. This would be the first time anyone has specifically looked for such a particle.