Charge-transfer (CT) states, bound combinations of an electron and a hole on separate molecules, play a crucial role in organic optoelectronic devices. We report direct nanoscale imaging of the transport of long-lived CT states in molecular organic donor-acceptor blends, which demonstrates that the bound electron-hole pairs that form the CT states move geminately over distances of 5-10 nm, driven by energetic disorder and diffusion to lower energy sites. Magnetic field dependence reveals a fluctuating exchange splitting, indicative of a variation in electron-hole spacing during diffusion. The results suggest that the electron-hole pair of the CT state undergoes a stretching transport mechanism analogous to an 'inchworm' motion, in contrast to conventional transport of Frenkel excitons. Given the short exciton lifetimes characteristic of bulk heterojunction organic solar cells, this work confirms the potential importance of CT state transport, suggesting that CT states are likely to diffuse farther than Frenkel excitons in many donor-acceptor blends.