Motor proteins of the kinesin family move actively along microtubules to transport cargo within cells. How exactly a single motor proceeds on the 13 narrow lanes or protofilaments of a microtubule has not been visualized directly, and there persists controversy on the relative position of the two kinesin heads in different nucleotide states. We have succeeded in imaging Kinesin-1 dimers immobilized on microtubules with single-head resolution by atomic force microscopy. Moreover, we could catch glimpses of single Kinesin-1 dimers in their motion along microtubules with nanometer resolution. We find in our experiments that frequently both heads of one dimer are microtubule-bound at submicromolar ATP concentrations. Furthermore, we could unambiguously resolve that both heads bind to the same protofilament, instead of straddling two, and remain on this track during processive movement.