The YORP effect is a small thermal-radiation torque experienced by small asteroids, and is considered to be crucial in their physical and dynamical evolution. It is important to understand this effect by providing measurements of YORP for a range of asteroid types to facilitate the development of a theoretical framework. We are conducting a long-term observational study on a selection of near-Earth asteroids to support this. We focus here on (68346) 2001 KZ66, for which we obtained both optical and radar observations spanning a decade. This allowed us to perform a comprehensive analysis of the asteroid's rotational evolution. Furthermore, radar observations from the Arecibo Observatory enabled us to generate a detailed shape model. We determined that (68346) is a retrograde rotator with its pole near the southern ecliptic pole, within a 15-degree radius of longitude 170 degrees and latitude -85-degrees. By combining our radar-derived shape model with the optical light curves we developed a refined solution to fit all available data, which required a YORP strength of (8.43+/-0.69)x10^-8^rad/day/day. (68346) has a distinct bifurcated shape comprising a large ellipsoidal component joined by a sharp neckline to a smaller non-ellipsoidal component. This object likely formed from either the gentle merging of a binary system, or from the deformation of a rubble pile due to YORP spin-up. The shape exists in a stable configuration close to its minimum in topographic variation, where regolith is unlikely to migrate from areas of higher potential.