The nonlinear dynamic response of polymer melt brushes to large amplitude oscillatory shear is studied using melt state rheology of end-tethered polymer layered-silicate nanocomposites. These model melt brushes exhibit reversible strain hardening at moderate strain amplitudes, characterized by the presence of a critical strain amplitude for the transition that is only a function of the interlayer distance (i.e., silicate fraction). These results differ qualitatively from those observed for solvent-filled polymer brushes. A phenomenological explanation based on stretching of already distorted chains in response to the applied shear and predicted on the space filing requirements of s melt brush is provided to explain these unique results.