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CrI3 has recently been shown to exhibit low-dimensional, long-range magnetic ordering from few layers to single layers of CrI3. The properties of CrI3 bulk and few-layered systems are uniquely defined by a combination of short-range intralayer and long-range interlayer interactions, including strong correlations, exchange, and spin-orbit coupling. Unfortunately, both the long-range van der Waals interactions, which are driven by dynamic, many-body electronic correlations, and the competing strong intralayer correlations, present a formidable challenge for the local or semilocal mean-field approximations employed in workhorse electronic structure approaches like density-functional theory. In this paper we employ a sophisticated many-body approach that can simultaneously describe long- and short-range correlations. We establish that the fixed-node diffusion Monte Carlo (FNDMC) method reproduces the experimental interlayer separation distance of bulk CrI3 for the high-temperature monoclinic phase with a reliable prediction of the interlayer binding energy. We subsequently employed the FNDMC results to benchmark the accuracy of several density-functional theory exchange-correlation approximations.