Tetramercaptotetrathiacalix[4]arene (LH4) can be used as a coordination platform to bind four CuI ions at the thiolate and thioether S atoms. Donor ligands such as phosphanes can stabilize the resulting [LCu4] units, which then remain monomeric ([(Ph3PCu)4L]). In the absence of donor ligands, they aggregate, providing a hexamer ([LCu4]6) in high yields, with a hollow‐sphere structure formed by an unprecedented Cu24S48 cage that is surrounded by the organic framework of the calixarene chalices. Preliminary NMR experiments with regard to the host‐guest chemistry in solution showed that the compound represents a polytopic host for acetonitrile and methane.