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What is producing the ultra-high energy (UHE) cosmic rays, the highest-energy particles in nature? While this question still has no definitive answer, the Pierre Auger experiment has hinted that the nearby radio galaxy Centaurus A might be the culprit. Onesmoking gun'would be the detection of a cosmic ray from Centaurus A of such an extreme energy that there could be no magnetic-field bending of the path. Another would be the detection of a UHE neutrino, since these particles are expected from both UHE cosmic ray interactions and production regions. Our collaboration has been perfecting-within the limits of current technology-the lunar Cherenkov technique, by which UHE particle interactions in the Moon may be detected by their GHz coherent radio emission. We propose to use this technique with the Parkes radio telescope to search for both UHE neutrinos and cosmic rays from Centaurus A.