One of the most important steps in tumor progression involves the transformation from a differentiated epithelial phenotype to an aggressive, highly motile phenotype, where tumor cells invade neighboring tissues. Invasion can occur either by isolated mesenchymal cells or by aggregates that migrate collectively and do not lose completely the epithelial phenotype. Here, we show that, in a three-dimensional cancer cell culture, collective migration of cells eventually leads to aggregation in large clusters. We present quantitative measurements of cluster velocity, coalescence rates, and proliferation rates. These results cannot be explained in terms of random aggregation. Instead, a model of chemotaxis-driven aggregation - mediated by a diffusible attractant - is able to capture several quantitative aspects of our results. Experimental assays of chemotaxis towards culture conditioned media confirm this hypothesis. Theoretical and numerical results further suggest an important role for chemotactic-driven aggregation in spreading and survival of tumor cells.