Processivity, the ability of single molecules to move continuously along a track, is a fundamental requirement of cargo-transporting molecular motors. Here, we investigate how cytoplasmic dynein, a homodimeric, microtubule-based motor, achieves processive motion. To do this, we developed a versatile method for assembling Saccharomyces cerevisiae dynein heterodimers, using complementary DNA oligonucleotides covalently linked to dynein monomers labeled with different organic fluorophores. Using two-color, single-molecule microscopy and high-precision, two-dimensional tracking, we find that dynein has a highly variable stepping pattern that is distinct from all other processive cytoskeletal motors, which use 'hand-over-hand' mechanisms. Uniquely, dynein stepping is stochastic when its two motor domains are close together. However, coordination emerges as the distance between motor domains increases, implying that a tension-based mechanism governs these steps. This plasticity may allow tuning of dynein for its diverse cellular functions.