The Geminiviridae is an extensive family of plant viruses responsible for economically devastating diseases in crops worldwide. Geminiviruses package circular, single-stranded DNA (ssDNA) genomes. The characteristic twinned or "geminate" particles, which consist of two joined, incomplete T = 1 icosahedra, are unique among viruses. We have determined the first structure of a geminivirus particle, the Nigerian strain of Maize streak virus (MSV-N), using cryo-electron microscopy and three-dimensional image reconstruction methods. The particle, of dimensions 220 x 380 A, has an overall 52-point-group symmetry, in which each half particle "head" consists of the coat protein (CP) arranged with quasi-icosahedral symmetry. We have modeled the MSV-N CP as an eight-stranded, antiparallel beta-barrel motif (a structural motif common to all known ssDNA viruses) with an N-terminal alpha-helix. This has produced a model of the geminate particle in which 110 copies of the CP nicely fit into the reconstructed density map. The reconstructed density map and MSV-N pseudo-atomic model demonstrate that the geminate particle has a stable, defined structure.