We describe a new technique for searching for slowly moving, supermassive magnetic monopoles employing a single thick slab of PS-10 acrylic scintillator at sea level. Monopoles would be identified by the abnormally wide photomultiplier-tube anode signal produced as they traverse the thick slab at very low velocity (approx.10/sup -3/ c). The scintillation response to supermassive monopoles is reviewed, and the results of a calculation of the response of PS-10 are presented. No monopole candidates were observed in 3852 h of running time, and a limit on the flux F of supermassive monopoles, F< or approx. =4.1 x 10/sup -13/ cm/sup -2/ sr/sup -1/ s/sup -1/ (single-event significance) for monopole velocities 6 x 10/sup -4/ c< or approx. =V <2.1 x 10/sup -3/ c, is set. This result is compared to other experimental limits and to theoretical limits on the flux.