I will describe a novel class of statistical ensembles we developed for the description of chaotic conformal field theories. These are generalisations of the usual random-matrix type theories used in the description of quantum chaotic many-body systems, and implement the kinematical as well as dynamical constraints of the CFT bootstrap. These novel statistical models take the form of distributions over random matrices and tensors. I will take some time to characterise the individual elements in terms of so-called “approximate CFTs”. Finally, I will discuss the concrete realisation of these ideas for 2D, large-c CFT and point out that the resulting tensor models (subject to reasonable constraints on the spectrum) take the form of an integral over random discrete triangularisation of 3D Euclidean manifolds, governed by the 6j symbols of Virasoro, strongly suggesting a connection to three dimensional quantum gravity.