In this contribution, we reported the synthesis of a hyperbranched block copolymer composed of poly(ε-caprolactone) (PCL) and polystyrene (PS) subchains. Toward this end, we first synthesized an α-alkynyl- and ω,ω′-diazido-terminated PCL-b-(PS)₂ macromonomer via the combination of ring-opening polymerization and atom transfer radical polymerization. By the use of this AB₂ macromonomer, the hyperbranched block copolymer (h-[PCL-b-(PS)₂]) was synthesized via a copper-catalyzed Huisgen 1,3-dipolar cycloaddition (i.e., click reaction) polymerization. The hyperbranched block copolymer was characterized by means of ¹H nuclear magnetic resonance spectroscopy and gel permeation chromatography. Both differential scanning calorimetry and atomic force microscopy showed that the hyperbranched block copolymer was microphase-separated in bulk. While this hyperbranched block copolymer was incorporated into epoxy, the nanostructured thermosets were successfully obtained; the formation of the nanophases in epoxy followed reaction-induced microphase separation mechanism as evidenced by atomic force microscopy, small angle X-ray scattering, and dynamic mechanical thermal analysis.