Living systems use chemical fuels to transiently assemble functional structures. As a step toward constructing abiotic mimics of such structures, we herein describe dissipative formation of covalent basket cage CBC 5 by reversible imine condensation of cup‐shaped aldehyde 2 (i.e. basket) with trivalent aromatic amine 4. This nanosized [4 4] cage (V=5 nm3, Mw=6150 Da) has shape of a truncated tetrahedron with four baskets at its vertices and four aromatic amines forming the faces. Importantly, tris‐aldehyde basket 2 and aliphatic tris‐amine 7 undergo condensation to give small [1 1] cage 6. The imine metathesis of 6 and aromatic tris‐amine 4 into CBC 5 was optimized to bias the equilibrium favouring 6. Addition of tribromoacetic acid (TBA) as a chemical fuel perturbs this equilibrium to result in the transient formation of CBC 5, with subsequent consumption of TBA via decarboxylation driving the system back to the starting state.