We report electroabsorption measurements of chi((3))(-omega; 0, 0, omega) for a new conjugated porphyrin polymer formed by the edge-linking of zinc porphyrin macrocyles through conjugated acetylenic bridges. The polymer is solution processed into thin film form and experiments performed on the films indicate a very large nonlinearity, an order of magnitude larger than we have previously measured in conjugated polymers such as poly(p-phenylene vinylene) and poly(2,5-thienylene vinylene). There is clear evidence of the extension of conjugation through the acetylenic bridges. Comparison is made between results obtained for the polymer, and its monomer and dimer analogues dispersed in an inert polymer matrix.