A measurement of the absorption of neutrinos with energies in excess of 10 TeV when traversing the Earth is capable of revealing its density distribution. Unfortunately, the existence of beams with sufficient luminosity for the task has been ruled out by the AMANDA South Pole neutrino telescope. In this Letter we point out that, with the advent of second-generation kilometer-scale neutrino detectors, the idea of studying the internal structure of Earth may be revived using atmospheric neutrinos instead.