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We have carried out quantum Monte Carlo (QMC) calculations to study the interlayer interaction in a boron nitride (BN) bilayer. The binding energy, 81 meV/2BN after finite-size corrections, was found to be larger than that obtained by density functional theory (DFT) with local density approximation, and smaller than those using van der Waals density functionals, both by considerable amounts. The QMC calculated interaction beyond the equilibrium interlayer separation was found to have a longer-range behavior than all the available DFT schemes.