A Born-Green-Yvon (BGY) integral equation approach is used to study the structure and thermodynamics of a fluid of fused hard sphere dimers. Starting from a BGY equation for the dimer molecular pair distribution function, an equation for the simpler site-site distribution is derived. The multisite distribution functions appearing in this latter equation are related to the site-site function via a set of superposition approximations. Detailed results are presented for dimers with bond lengths of L = 0.6sigma and 1.0sigma (where sigma is the hard sphere site diameter). These results, which include the site-site distribution function over a range of densities, as well as the virial and compressibility pressure equations of state, are compared with analytic and Monte Carlo results.