The chromosomal segregation machinery in bacteria such as Caulobacter crescentus and Bacillus subtilis includes the ParABS partitioning system. This segregation machinery includes a large ParB-DNA complex, localized near the origin of replication on the chromosome, consisting of ~1000 ParB proteins clustered around one or a few centromeric parS sites. During segregation the ParB-DNA complex associates with a ParA spindle-like apparatus. Despite the apparent simplicity of this segregation machinery, puzzles remain: What is the nature of interactions among DNA-bound ParB proteins, and how do these determine the organizational and functional properties of the ParB-DNA partitioning complex? A crucial aspect of this question is whether ParB spreads along the DNA to form a filamentous complex with a one-dimensional character, or rather aggregates to form a three-dimensional complex on the DNA. Furthermore, it remains unclear how the presence of only one or even a few centromeric parS sites can lead to robust formation and localization of a large protein-DNA complex. We developed a simple model for interacting proteins on DNA and found that a combination of 1D spreading bonds and a single 3D bridging bond between ParB proteins constitutes the minimal model for condensation of a three-dimensional ParB-DNA complex. These combined interactions provide an effective surface tension that prevents fragmentation of the ParB-DNA complex. Thus, conceptually, the partitioning complex is described as a 3D ParB-DNA condensate, which is formed through a phase transition.