Solar coronal mass ejections (CMEs) are the most significant drivers of adverse space weather on Earth, but the physics governing their propagation through the heliosphere is not well understood. Although stereoscopic imaging of CMEs with NASA's Solar Terrestrial Relations Observatory (STEREO) has provided some insight into their three-dimensional (3D) propagation, the mechanisms governing their evolution remain unclear because of difficulties in reconstructing their true 3D structure. In this paper, we use a new elliptical tie-pointing technique to reconstruct a full CME front in 3D, enabling us to quantify its deflected trajectory from high latitudes along the ecliptic, and measure its increasing angular width and propagation from 2 to 46 (∼0.2 AU). Beyond 7 , we show that its motion is determined by an aerodynamic drag in the solar wind and, using our reconstruction as input for a 3D magnetohydrodynamic simulation, we determine an accurate arrival time at the Lagrangian L1 point near Earth.