The black phosphorus (black-P) crystal is formed of covalently bound layers of phosphorene stacked together by weak van der Waals interactions. An experimental measurement of the exfoliation energy of black-P is not available presently, making theoretical studies the most important source of information for the optimization of phosphorene production. Here, we provide an accurate estimate of the exfoliation energy of black-P on the basis of multilevel quantum chemical calculations, which include the periodic local Moller-Plesset perturbation theory of second order, augmented by higher-order corrections, which are evaluated with finite clusters mimicking the crystal. Very similar results are also obtained by density functional theory with the D3-version of Grirnme's empirical dispersion correction. Our estimate of the exfoliation energy for black-P of -151 meV/atom is substantially larger than that of graphite, suggesting the need for different strategies to generate isolated layers for these two systems.