Aims. We report and analyse the first observation of a transverse oscillation in a hot coronal loop with the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO), following a linked coronal-flare mass-ejection event on the 3 November 2010. The oscillating coronal loop is observed off the east solar limb and exclusively in the 131 Å and 94 Å bandpasses, indicating a loop plasma of temperature in the range of 9-11 MK. Furthermore, the loop is not observed to cool into the other AIA channels, but just disappears from all bandpasses at the end of the oscillation. Methods. A time series analysis of the loop oscillation is conducted by taking several cuts at different positions along the loop, estimating the transverse displacements over time for two strands in the loop and fitting those with a damped cosine curve. Intensity time variations, both along the loop and for a series of cut cross-sections, are investigated. Using a three-dimensional loop geometry obtained from a comparison of STEREO-B/EUVI and AIA images, we model different modes of transverse oscillations in the uniformly filled loop. Results. Our time series analysis reveals a period of 302 ± 14 s (291 ± 9 s) and a damping time of 306 ± 43 s (487 ± 125 s) for the first (second) loop strand. A spatial phase shift along the loop of approximately 180 • suggests that we observe a higher order harmonic. Intensity oscillations are consistent with an interpretation in terms of a vertically polarised mode. Our forward modelling suggests that the loop oscillates as either a second or third order harmonic of this mode. Conclusions. This is the first observation of a transverse loop oscillation observed exclusively in the hot coronal lines. The loop oscillation is vertically polarised and is dominated by a higher order harmonic mode. We conclude that the excitation mechanism of this 5 min period oscillation is directly connected with the reconnection processes that form the post flare loop, which differs from the blast wave excitation mechanism often proposed as the cause of cooler transverse loop oscillations.