Cytoplasmic dynein is a motor protein that walks along microtubules (MTs) and performs mechanical work to power a variety of cellular processes. It remains unclear how a dynein dimer is able to transport cargos against load without coordinating the stepping cycles of its two heads. Here by using a DNA-tethered optical trapping geometry, we find that the force-generating step of a head occurs in the MT-bound state, while the 'primed' unbound state is highly diffusional and only weakly biased to step towards the MT-minus end. The stall forces of the individual heads are additive, with both heads contributing equally to the maximal force production of the dimer. On the basis of these results, we propose that the heads of dynein utilize a 'load-sharing' mechanism, unlike kinesin and myosin. This mechanism may allow dynein to work against hindering forces larger than the maximal force produced by a single head.