A new method is proposed to detect mantle plumes in the lower mantle. The method is akin to diffraction tomography, and relies on the scattering of long-period seismic body waves by nearly vertical heterogeneities. The theory is described in a companion paper [Ying Ji, H.-C. Nataf, Earth Planet. Sci. Lett., this issue]. Here we apply this method to an actual set of long-period digital seismograms recorded on the world-wide network of seismic stations between 1980 and 1994. We select seismograms that `illuminate' the lower mantle in a 20°×20° region around Hawaii. We construct an image of `plume-like' heterogeneities, using a cell size of 1°×1°, by a LSQR inversion of the scattered waves. This image shows a strong slow anomaly about 200 km northwest of Hawaii. Although the image is somewhat noisy, resolution tests indicate that this feature is fairly robust. The amplitude of the anomaly is between 30 and 60 times larger than what we predict from a simple thermal plume model, built with a 600 K maximum temperature excess, and a gaussian horizontal cross-section with an 1/ e diameter of 250 km. It is the first time that such a method is applied to the mantle. While we think that the existence of this anomaly is real, we do not know how to explain such a large amplitude. If real, this observation has a number of important geodynamical consequences. It indicates that a mantle plume is indeed responsible for the Hawaii hotspot, as speculated by Morgan [W.J. Morgan, Nature 230 (1971) 42-43]. The plume is nearly vertical. It originates from the D″ region, at the base of the lower mantle. The amplitude of the anomaly suggests that partial melt or/and a chemical anomaly must be present. The plume source is to the northwest of its surface expression, as predicted by some models of plume advection in the `mantle wind'.