Three-arm star block copolymers have been synthesized from linear polystyrene (PS) and poly(g-caprolactone) (PCL) building blocks. Through the use of an alpha-diene-omega-alkyne functionalized PCL, the PS-b-PCL stars have been synthesized via either forming the PS-b-PCL arms first with the hetero Diels-Alder (HDA) cycloaddition and their subsequent coupling to a triazide coupling agent through a copper(I) -catalyzed azide-alkyne cycloaddition (CuAAC) (arm-first) or via forming the basic star structure first through the CuAAC of the coupling agent and the PCL, with the diblock stars achieved by the subsequent HDA cycloaddition with the PS, (corefirst). The use of the two consecutive reactions has facilitated high conversions and a good control over the multiple reaction sites. In both examples, the CuAAC proceeded to quantitative conversion whereas the HDA cycloaddition proceeded to 94% conversion in the arm-first approach and 81% in the core-first approach.