Measurement-based quantum computing, a powerful alternative to the standard circuit model, proceeds using only local adaptive measurements on a highly-entangled resource state of many spins on a graph or lattice. Along with the canonical cluster state, the valence-bond solid ground state on a chain of spin-1 particles, studied by Affleck, Kennedy, Lieb, and Tasaki (AKLT), is such a resource state. We propose a simulation of this AKLT state using linear optics, wherein we can make use of the high-fidelity projective measurements that are commonplace in quantum optical experiments, and describe how quantum logic gates can be performed on this chain. In our proposed implementation, the spin-1 particles comprizing the AKLT state are encoded on polarization biphotons: three level systems consisting of pairs of polarized photons in the same spatio-temporal mode. A logical qubit encoded on the photonic AKLT state can be initialized, read out and have an arbitrary single qubit unitary applied to it by performing projective measurements on the constituent biphotons. For MBQC, biphoton measurements are required which cannot be deterministically performed using only linear optics and photodetection. Comment: 9 pages, 4 figures, published version