Observations of the natural variability in the structure of seismic discontinuities in Earth's mantle can be used to infer spatial variations in temperature and composition. Here I present a high-resolution analysis of converted seismic waves from the olivine-wadsleyite phase transition beneath Rarotonga, Cook Islands. New advances in seismic signal processing permit the determination of local variations in phase transition thickness in addition to variations in absolute depth. I find that the depth and thickness of the phase transition vary systematically underneath the island, and further that temperature alone is insufficient to explain these observations. A chemical anomaly is required, consistent with the presence of a plume in the mantle.