The classic nanocomposite approach aims at percolation of low fraction of exfoliated individual reinforcing nanoscale elements within a polymeric matrix. By contrast, many of the mechanically excellent biological nanocomposites involve self-assembled and space-filled structures of hard reinforcing and soft toughening domains, with high weight fraction of reinforcements. Here we inspect a new concept toward mimicking such structures by studying whether percolation of intercalated domains consisting of alternating rigid and reinforcing, and soft rubbery domains could allow a transition to a reinforced state. Toward that, we present the functionalization of rigid native cellulose nanocrystals (CNCs) by esterification with a dense hydrocarbon chain brush containing cross-linkable double bonds. Composite films with 0-80 wt % of such modified CNCs (mCNCs) within a poly(butadiene) (PBD) rubber matrix were prepared via cross-linking by UV-light initiated thiol-ene click reaction. Transmission electron microscopy showed structures at two length scales, where the mCNCs and PBD form domains having internal aligned self-assemblies of alternating hard mCNCs and soft PBD with periodicity of ca. 40 nm, and where additional PBD connects such domains. Increasing the weight fraction of mCNCs causes an uncommon abrupt transition from PBD-dominated soft materials to significantly reinforced mCNC-dominated mechanical properties, suggesting that the intercalated self-assembled mCNC/PBD domains percolate in PBD upon passing 30-35 wt % of mCNCs. Maximum stress of 16 MPa at mCNC fraction of 80 wt % was obtained. The mechanical properties of the composites show exceptional insensitivity to air humidity. The shown simple concept of percolative intercalated nanocomposites suggests searching for more general biomimetic compositions involving several deformation mechanisms for improved mechanical properties.