A miktoarm star-shaped copolymer, with one polystyrene arm (M-w = 198 kg/mol) and three polyisoprene arms (M-w = 51 kg/mol) (PSPI3), was rigorously characterized by temperature gradient interaction chromatography (TGIC). The polymer was prepared by linking active chain ends of precursor polymers to tetrachlorosilane as the linking agent, and the precursor polymers were prepared by anionic polymerization. The crude product was purified by fractional precipitation to remove the byproducts and the excess reagents. Size exclusion chromatography (SEC) analysis shows a narrow single elution peak whose molecular weight and composition are in good agreement with the predicted values in experimental precision. Therefore, it appears on the basis of conventional characterization using SEC, light scattering, and NMR that the fractionated mother represents a high-purity PSPI3 miktoarm star copolymer. However, TGIC analysis reveals the presence of significant amount of byproducts, most significantly PSPI2, which amounts to about 20% of the fractionated sample. This result clearly indicates that the analysis results utilizing conventional polymer characterization tools such as SEC, light scattering, osmometry, and viscometry are insufficient to establish the purity of polymers with complex architecture. It seems preferable to carry out a more detailed analysis such as that described in this work, in particular for polymers with complex architectures, if rigorous proof of structural purity is required.