A number of recent transport and magnetization studies have shown signs of ferromagnetism in the LaAlO3/SrTiO3 heterostructure(1-6), 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(7-11). 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 Ti3+ character in the d(xy) orbital of the anisotropic t(2g) band. These findings establish a striking example of emergent phenomena at oxide interfaces.