Myxobacteria provide one of the simplest models of cell-cell interaction and organized cell movement leading to cellular differentiation. When starved, tens of thousands of cells change their movement pattern from outward spreading to inward concentration; they form aggregates that become fruiting bodies. Cells inside fruiting bodies differentiate into round, non-motile, environmentally resistant spores. Traditionally, cell aggregation has been considered to imply chemotaxis - a long-range cell interaction. However, myxobacterial aggregation is the consequence of direct cell-contact interactions, not chemotaxis. We present here the first three-dimensional (3D) stochastic lattice-gas cellular automata (LGCA) model of cell aggregation based on local cell-cell contact, and no chemotaxis. We demonstrate that a 3D discrete stochastic model can simulate two stages of cell aggregation. First, a 'traffic jam' forms embedded in a field of motile cells. The jam then becomes an aggregation center that accumulates more cells. We show that, at high cell density, cells stream around the traffic jam, generating a three-dimensional hemispherical mound. Later, when the nuclear traffic jam dissolves, the aggregation center becomes a 3D ring of streaming cells.