As the smallest and simplest motor enzymes, kinesins have served as the prototype for understanding the relationship between protein structure and mechanochemical function of enzymes in this class. Conventional kinesin (kinesin-1) is a motor enzyme that transports cargo toward the plus end of microtubules by a processive, asymmetric hand-over-hand mechanism. The coiled-coil neck domain, which connects the two kinesin motor domains, contributes to kinesin processivity (the ability to take many steps in a row) and is proposed to be a key determinant of the asymmetry in the kinesin mechanism. While previous studies have defined the orientation and position of microtubule-bound kinesin motor domains, the disposition of the neck coiled-coil remains uncertain. We determined the neck coiled-coil orientation using a multidonor fluorescence resonance energy transfer (FRET) technique to measure distances between microtubules and bound kinesin molecules. Microtubules were labeled with a new fluorescent taxol donor, TAMRA-X-taxol, and kinesin derivatives with an acceptor fluorophore attached at positions on the motor and neck coiled-coil domains were used to reconstruct the positions and orientations of the domains. FRET measurements to positions on the motor domain were largely consistent with the domain orientation determined in previous studies, validating the technique. Measurements to positions on the neck coiled-coil were inconsistent with a radial orientation and instead demonstrated that the neck coiled-coil is parallel to the microtubule surface. The measured orientation provides a structural explanation for how neck surface residues enhance processivity and suggests a simple hypothesis for the origin of kinesin step asymmetry and "limping."