Ab initio calculations of the static longitudinal second hyperpolarizability of molecular hydrogen model chains have been performed at different levels of approximation to investigate the effects of including electron correlation, as well as the variation of these effects as a function of the atomic basis set. Inclusion of electron correlation within the Moller-Plesset schemes limited to second (MP2), third (MP3), and fourth (MP4) order in electron-electron interactions leads to an increase of the longitudinal second hyperpolarizability per unit cell which is mainly due to the second-order correction provided that a sufficiently extended basis set is used. Indeed, whereas the basis set does not influence significantly the UCHF and CHF values, a too small basis set underestimates the positive second-order contribution, overestimates the negative third-order contribution and leads to a fourth-order contributions having an incorrect sign. This positive electron correlation correction for the second hyperpolarizability is opposite to the negative correction brought to the static longitudinal polarizability per unit cell for which the CHF level with a split-valence basis set provides reliable polarizability estimates. The present investigation points out that good estimates of the second hyperpolarizability are already obtained by using the MP2 procedure with a sufficiently extended basis set.