We report a dynamic self-assembly system of "living" polymeric chains sustained by chemistry using reactive molecular dynamics simulations. The linear polymeric chains consist of self-assembled nanoparticles connected by metastable linker molecules. As such, the polymeric chains, once assembled, undergo spontaneous dissociation driven by thermodynamics. However, with a continuous supply of linker molecules and the stored chemical energy therein, the polymeric chains can survive and maintain a steady state averaged chain length. These dynamically self-assembled polymeric chains are analogous to biological systems that both are thermodynamically metastable, yet dynamically stable upon continuous influx of matter and energy.