Recent observation of efficient light emission from porous silicon has attracted much attention and renewed interests in the study of nonlinear optical properties of nanometer-sized quantum systems. In this paper, we study the third-order nonlinear optical susceptibility of semiconductor quantum wires. The quantum wires are taken to be circular columns with a cross section size of \ensuremath{\sim}1 nm. The excitonic effects are taken to be the major electronic excitations. We find that the quantum confinement of the excitons greatly enhances the third-order optical nonlinear susceptibility in a quantum wire. The source of the enhancement is primarily the confinement-induced localization of excitons. The large enhancement of the third-order optical nonlinearity estimated here is consistent with the recent observation of the efficient infrared-up-conversion luminescence in porous silicon.