The generation and detection of maximally-entangled two-particle states, `Bell states', are crucial tasks in many quantum information protocols such as cryptography, teleportation, and dense coding. Unfortunately, they require strong inter-particle interactions lacking in optics. For this reason, it has not previously been possible to perform complete Bell state determination in optical systems. In this work, we show how a recently developed quantum interference technique for enhancing optical nonlinearities can make efficient Bell state measurement possible. We also discuss weaknesses of the scheme including why it cannot be used for unconditional quantum teleportation.