A Direct Search for Magnetic Monopoles at HERA ---------------------------------------------- A direct search has been made for magnetic monopoles produced in e+ p collisions at a centre of mass energy of 300 GeV at HERA. The beam pipe surrounding the interaction region during 1995-1997 (integrated luminosity 60 pb-1) was investigated using a SQUID magnetometer to look for stopped magnetic monopoles. No free magnetic charges were observed and charge-dependent upper limits on the cross section for the electro-production of magnetic monopoles have been set.