In this work, we present three new branched chain equations of state (EOS) based on Wertheimﾒs perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheimﾒs second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a LennardﾖJones dimer reference system to obtain an equation of state for branched LennardﾖJones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.