The mechanism of destabilization of rotating vortices of chemical activity (scroll waves) induced by a parameter gradient is studied in a gel-immobilized Belousov-Zhabotinsky (BZ) reaction. Destabilization occurs when a temperature gradient above a certain critical value is applied parallel to the filament of an initially simple scroll wave. Direct observation of the vortex filament using video imaging provides evidence that the mechanism of destabilization involves the spontaneous creation of a helical perturbation of the filament which grows and eventually collides with the boundaries of the medium, fragmenting into multiple filaments. Evidence is presented that is phenomenon is the result of an instability caused by a gradient-induced filament drift.