We find that first-order thermodynamic perturbation theory (TPT1) which incorporates the reference monomer fluid used in the generalized Flory-AB (GF-AB) theory yields an equation of state for fused hard-sphere (FHS) chain fluids that has accuracy comparable to the GF-AB and GF-dimer-AC theories. The new TPT1 equation of state is significantly more accurate than other extensions of the TPT1 theory to FHS chain fluids. The TPT1 is also extended to two-dimensional fused hard-disk chain fluids. For the fused hard-disk dimer fluid, the extended TPT1 equation of state is found to be more accurate than the Boublik hard-disk dimer equation of state.