Recent theory and numerical simulation predicts that the wake of the solar wind flow past the Moon should be the site of electrostatic instabilities that give rise to electron holes. These play an important role in the eventual merging of the wake with the background solar wind. Analysis of measurements from the ARTEMIS satellites, orbiting the Moon at distances from 1.2 to 11 R-M, detects holes highly concentrated in the wake, in agreement with prediction. The theory also predicts that the hole flux density observed should be hollow, peaking away from the wake axis. Observation statistics qualitatively confirm this hollowness, lending extra supporting evidence for the identification of their generation mechanism. Plain Language Summary Analysis of measurements by the ARTEMIS satellites orbiting the Moon shows that, in the lunar plasma wake, isolated electric structures called electron holes are being continuously formed. These holes are regions of depleted electron density that are maintained by their own positive charge. As the solar wind flows supersonically past the Moon, a density-depleted wake of approximate length 20,000 km (10 lunar radii) forms behind it. Plasma streams along the magnetic field fill in the wake, and theory predicts that instabilities should occur giving rise to these holes. They are solitary waves (solitons) consisting of short electric potential humps of width approximately 100 m. Motivated by this theory, ARTEMIS measurements of rapid variations of the electric field around the satellite have been searched for the characteristic signatures of holes. It is found that holes occur extremely frequently when the satellites are in the wake, but only very rarely outside the wake, and that in accordance with theory, the holes occur less frequently at the wake center than part-way out.