Thermodynamic perturbation theory of the first order (TPT1) is extended to heterobonded chains, such as heteronuclear and branched copolymers. The TPT1 formalism provides the basis for a copolymer equation of state. This new copolymer equation of state, referred to as Copolymer SAFT (Statistical Associating Fluid Theory), explicitly accounts for the effects of chain heterogeneity and microstructure. In order to illustrate potential future applications, Copolymer SAFT is used to calculate high-pressure cloud points in real polymer solutions of supercritical propane + poly(ethylene-co-butene).