The compressibility factor of nonassociated chain molecules composed of hard convex core Yukawa segments was derived with SAFT-VR and an extension of the Barker-Henderson perturbation theory for convex bodies. The temperature-dependent chain and dispersion compressibility factors were derived using the Yukawa potential. The effects of temperature, packing fraction, and segment number on the compressibility factor were investigated for chains of the prolate sphereocylinder segments. A comparison of hard core Yukawa chain compressibility factor values and hard chain compressibility factor values showed that the type of interaction potential has more effect on those chain molecules with higher segment numbers. The results demonstrated that in reduced temperatures 1.4 and 2.4, the Yukawa chain of the compressibility factor is insensitive to temperature, while the dispersion term of the compressibility factor changes remarkably with the temperature. The derived equation of state can fairly predict the SAFT-VR results of the hard sphere core chain molecules in the limit of α = 1.