The electronic reconstruction at the interface between two insulating oxides can give rise to a highly conductive interface. Here we show how, in analogy to this remarkable interface-induced conductivity, magnetism can be induced at the interface between the otherwise non-magnetic insulating perovskites SrTiO3 and LaAlO3. A large negative magnetoresistance of the interface is found, together with a logarithmic temperature dependence of the sheet resistance. At low temperatures, the sheet resistance reveals magnetic hysteresis. Magnetic ordering is a key issue in solid-state science and its underlying mechanisms are still the subject of intense research. In particular, the interplay between localized magnetic moments and the spin of itinerant conduction electrons in a solid gives rise to intriguing many-body effects such as Ruderman-Kittel-Kasuya-Yosida interactions, the Kondo effect and carrier-induced ferromagnetismin diluted magnetic semiconductors. The conducting oxide interface now provides a versatile system to induce and manipulate magnetic moments in otherwise non-magnetic materials.