A number of recent transport and magnetization studies have shown signs of ferromagnetism in the LaAlO3/SrTiO3 heterostructure, an unexpected property with no bulk analogue in the constituent materials. However, no experiment thus far has provided direct information on the host of the magnetism. Here we report spectroscopic investigations of the magnetism using element-specific techniques, including X-ray magnetic circular dichroism and X-ray absorption spectroscopy, along with corresponding model calculations. We find direct evidence for in-plane ferromagnetic order at the interface, with Ti(3+) character in the dxy orbital of the anisotropic t2g band. These findings establish a striking example of emergent phenomena at oxide interfaces.