Localized anharmonic rattling of Al atoms in VAl<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mrow><mml:mn>10.1</mml:mn></mml:mrow></mml:msub></mml:math>

We have used a suite of diffraction, thermodynamic, and transport measurements to study the localized rattling of Al guest atoms in VAl${}_{10.1}$. The mean-square displacement of the rattling atom shows a concave-down temperature dependence. This is characteristic of an anharmonic vibration, the frequency of which increases with amplitude, akin to a particle in a box. We find that the rattling is best described in terms of a sixth-order interatomic potential, with negligible contributions from harmonic and quartic terms. The rattler has a characteristic temperature of ${\ensuremath{\theta}}_{RM}=21$ K and couples strongly to both the acoustic phonons and conduction electrons. The coupling to the phonons is evident from the large value of the Gr\"uneisen parameter, which increases with decreasing temperature to $\ensuremath{\Gamma}\ensuremath{\approx}43$ at 5 K. Below 6 K, the electrical resistivity varies as ${T}^{3}$, which can be explained in terms of electron scattering from damped sixth-order vibrations. VAl${}_{10.1}$ is a superconductor below ${T}_{c}=1.53$ K, with an upper critical field of $\ensuremath{\sim}$1 kG.