This paper argues that a global large eddy simulation can be achieved through the application of the superparametrization (SP) methodology on massively parallel computers. SP was proposed over 15 years ago to improve the representation of deep convection and accompanying small-scale processes in large-scale models for the weather and climate. The main idea was to embed in all columns of the large-scale model (featuring horizontal grid lengths of the order of 100 km) a two-dimensional (2D) convection-permitting small-scale model with approximately a 1-km horizontal grid length and periodic lateral boundaries. We propose to expand this methodology by applying a high-spatial-resolution three-dimensional (3D) large-eddy simulation (LES) model as the SP model and by embedding it in all columns of a large-scale model with a horizontal grid length in the range of 10 to 50 km. The outer model can apply hydrostatic equations as typical global numerical weather prediction and climate models today and can simulate atmospheric processes down to the mesoscale, including organized convection. Small-scale processes, such as boundary-layer turbulence and convective drafts, can be simulated by embedded nonhydrostatic (e.g., anelastic) LES models. Although significantly more expensive than the traditional SP, SP LES is ideally suited to take advantage of parallel computation because of the minimal communication between LES models when compared to traditional domain-decomposition methodologies in parallel simulation. Moreover, as illustrated through the idealized 2D mock-Hadley cell simulations, LES models can feature different horizontal and vertical grids in various columns of the large-scale model, and thus target dominant cloud regimes in various geographical regions. Such a system allows an unstructured grid simulation with no additional model development.