Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are essential operations in quantum information science. We propose and demonstrate the projection of two quantum three state systems (qutrits) onto a generalized maximally entangled state. These qutrits are represented by the polarization of pairs of indistinguishable photons, biphotons. The projection is a joint measurement on both biphotons using standard linear optics elements. A basis of nine maximally entangled states is presented that generalize the Bell basis for qubits. We explicitly show that our scheme can discriminate one out of the nine states. The successful projection is announced by coincidence detection of all four photons involved by single photon detectors. This demonstration can enable the realization of qutrit teleportation, entanglement swapping and other such extensions for quantum information protocols.