Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, LaAlO3 (LAO) and SrTiO3 (STO), a system that has been studied intensively recently. Magnetoresistance, Hall and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity: one associated with Ti ions that is responsible for ferromagnetism, and a second associated with oxygen vacancies in the STO that is responsible for superconductivity.