Mixing γ-cyclodextrin (γ-CD), cucurbit[6]uril (CB[6]) and tetraammonium-bearing axles together led to a spontaneous formation of γ-CD-CB[6]-cowheeled [4]pseudorotaxanes. The well-defined unsymmetrical cavities thus formed enhance the binding affinity towards chiral amines by factors of several hundreds and show remarkably improved chiral discrimination.