Cellulose nanocrystals (CNCs) are naturally sourced elongated nanocolloids that form cholesteric phases in water and apolar solvents. It is well accepted that CNCs are made of bundles of crystalline microfibrils clustered side-by-side, and there is growing evidence that each individual microfibril is twisted. Yet, the origin of the chiral interactions between CNCs remains unclear. In this work, CNCs are described with a simple model of chiral hard splinters, enabling the prediction of the pitch using density functional theory and Monte Carlo simulations. The predicted pitch P compares well with experimental observations in cotton-based CNC dispersions in apolar solvents using surfactants but also with qualitative trends caused by fractionation or tip sonication in aqueous suspensions. These results suggest that the bundle shape induces an entropy-driven chiral interaction between CNCs, which is the missing link in explaining how chirality is transferred from the molecular scale of cellulose chains to the cholesteric order.