The discovery of current-switchable bi-stable remanent domain configurations on small ferromagnetic islands is reported. Rectangular NiFe islands with a thickness of 50 to 100 nm and lateral dimensions on the order of several microns were imaged using magnetic force microscopy after application of 10 ns current pulses through the material. The closure configuration can be set into either the 4 or 7 domain configuration by applying positive or negative current polarity at density on the order 107 A/cm2. The chirality of the closure patterns is fixed, implying that only two rather than four states are stable in these patterns. The possibility of using these configurations as a means of storing a logic state for memory applications is discussed.