Polyacetylene (PA) polymers -(-CH=CH-) N - lead to large second hyperpolarizabilities (γ) that increase with N. For small N the increase is quite rapid, eventually saturating (becoming linear in N) for N N γ s a t . Both experimental and theoretical attempts have been made to estimate N γ s a t . In 1994 this led to two Science papers, one obtainingN γ s a t = 20 (semiempirical theory) and the other obtaining N γ s a t = 125 (experiment, but on a substituted disordered form of PA!). We report here ab initio calculations up through N = 49 (C 9 8 H 1 0 0 ) and show that N γ s a t = 45 ± 5. The much larger experimental value, N γ s a t = 125, is explained in terms of the structural defects and disorder introduced by the synthetic method.