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Our current work has just been published in the Journal "Angewandte Chemie". In this work, exceptionally coherent and transparent hybrid Bragg stacks made of strictly alternating mica‐type nanosheets (synthetic hectorite) and polymer layers (polyvinylpyrrolidone) were fabricated at large scale. Distinct from ordinary nanocomposites, these stacks display long‐range periodicity, which is tunable down to angstrom precision. A large thermal transport anisotropy (up to 38) is consequently observed, with the high in‐plane thermal conductivity (up to 5.7 W m−1 K−1) exhibiting an effective medium behavior. The unique hybrid material combined with advanced characterization techniques allows correlating the full elastic tensors to the direction‐dependent thermal conductivities. We, therefore, provide a first analysis on how the direction‐dependent Young's and shear moduli influence the flow of heat.