A goal of biomimetic chemistry is to use the hierarchical architecture inherent in biological systems to guide the synthesis of functional three-dimensional structures. Viruses and other highly symmetrical protein cage architectures provide defined scaffolds to initiate hierarchical structure assembly. Here we demonstrate that a cross-linked branched polymer can be initiated and synthesized within the interior cavity of a protein cage architecture. Creating this polymer network allows for the spatial control of pendant reactive sites and dramatically increases the stability of the cage architecture. This material was generated by the sequential coupling of multifunctional monomers using click chemistry to create a branched cross-linked polymer network. Analysis of polymer growth by mass spectrometry demonstrated that the polymer was initiated at the interior surface of the cage at genetically introduced cysteine reactive sites. The polymer grew as expected to generation 2.5 where it was limited by the size constraints of the cavity. The polymer network was fully cross-linked across protein subunits that make up the cage and extended the thermal stability for the cage to at least 120 degrees C. The introduced reactive centers were shown to be active and their number density increased with increasing generation. This synthetic approach provides a new avenue for creating defined polymer networks, spatially constrained by a biological template.