We show that silver(I) hexacyanocobaltate(III), Ag₃Co(CN)₆, exhibits positive and negative thermal expansion an order of magnitude greater than that seen in other crystalline materials. This framework material expands along one set of directions at a rate comparable to the most weakly bound solids known. By flexing like lattice fencing, the framework couples this to a contraction along a perpendicular direction. This gives negative thermal expansion that is 14 times larger than in ZrW₂O₈. Density functional theory calculations quantify both the low energy associated with this flexibility and the role of argentophilic (Ag⁺...Ag⁺) interactions. This study illustrates how the mechanical properties of a van der Waals solid might be engineered into a rigid, useable framework.