The issue of multiple equilibrium phases in compositionally heterogeneous random copolymers is studied with an ethylene-butene copolymer representative of many linear low-density polyethylenes (LLDPE). This material has a dispersed minority phase (volume fraction f(beta) almost-equal-to 0.02) of highly branched, amorphous chains. A thermodynamic calculation of the equilibrium liquid state is done using the distribution of chain branching from temperature rising elution fractionation and the Flory-Huggins interaction parameter chi(AB) for linear and ethyl branched C4H8 repeat units. The calculation indicates that this copolymer is metastable, between the binodal and spinodal at a melt temperature of 150-degrees-C. The predicted volume fraction of the second phase, f(beta) = 0.016, is in good agreement with experiment. This work is the first to compare directly the observed and calculated two-phase behaviors in a random copolymer.