An equation of state for chain fluids has been derived through the r-particle cavity-correlation function (CCF) for chains obtained from sticky spheres; here r is the chain length. The r-particle CCF is approximated by a product of effective two-particle CCFs, accounting for nearest-neighbor correlations and next-to-nearest-neighbor correlations. For hard-sphere chain fluids (HSCF), the density dependence for nearest-neighbor effective two-particle CCFs is determined by the equation of Tildesley-Streett for hard-sphere dumbbells and that for next-to-nearest-neighbor effective two-particle CCFs by computer-simulation results for hard-sphere trimers. The final equation of state has a simple form which gives compressibility factors and second virial coefficients for homonuclear HSCFs covering a wide range of chain length (up to r=201) in excellent agreement with computer simulations. Satisfactory comparisons are also obtained between predicted and computer-simulation results for homonuclear HSCF mixtures, HSCFs containing side-chains and rings, and heteronuclear HSCFs (copolymers).