Regulation of T-cell activity is dependent on antigen-independent co-stimulatory signals provided by the disulphide-linked homodimeric T-cell surface receptors, CD28 and CTLA-4 (ref. 1). Engagement of CD28 with B7-1 and B7-2 ligands on antigen-presenting cells (APCs) provides a stimulatory signal for T-cell activation, whereas subsequent engagement of CTLA-4 with these same ligands results in attenuation of the response. Given their central function in immune modulation, CTLA-4- and CD28-associated signalling pathways are primary therapeutic targets for preventing autoimmune disease, graft versus host disease, graft rejection and promoting tumour immunity. However, little is known about the cell-surface organization of these receptor/ligand complexes and the structural basis for signal transduction. Here we report the 3.2-A resolution structure of the complex between the disulphide-linked homodimer of human CTLA-4 and the receptor-binding domain of human B7-2. The unusual dimerization properties of both CTLA-4 and B7-2 place their respective ligand-binding sites distal to the dimer interface in each molecule and promote the formation of an alternating arrangement of bivalent CTLA-4 and B7-2 dimers that extends throughout the crystal. Direct observation of this CTLA-4/B7-2 network provides a model for the periodic organization of these molecules within the immunological synapse and suggests a distinct mechanism for signalling by dimeric cell-surface receptors.