A new radial distribution function (RDF) for the Lennard-Jones (LJ) fluid is derived around the LJ potential size (sigma). The theoretically based RDF is completely analytical and real. Comparisons with computer simulation data at various conditions indicate that the RDF is. very accurate at r < 1.2 sigma; and the accuracy is consistent from low to high densities. The new RDF is utilized to study associating LJ chains by combining with Wertheim's first-order perturbation theory. The resulting equation of state is tested against computer simulation data for second virial coefficient and pressure of LJ chains, and for pressure and the fraction of non-associating molecules in associating LJ chains. The calculated results indicate that the new equation of state is very satisfactory and its performance is comparable to several empirical equations reported in the literature. Another feature of the new equation of state is that both chain bonding and association sites are adjustable for practical purposes.