The UK-built Chandrayaan-1 X-ray Spectrometer (C1XS) will fly as an ESA instrument on India's Chandrayaan-1 mission to the Moon, launched in October 2008. C1XS builds on experience gained with the earlier D-CIXS instrument on SMART-1, but will be a scientifically much more capable instrument. Here we describe the scientific objectives of this instrument, which include mapping the abundances of the major rock-forming elements (principally Mg, Al, Si, Ti, Ca and Fe) in the lunar crust. These data will aid in determining whether regional compositional differences (e.g., the Mg/Fe ratio) are consistent with models of lunar crustal evolution. C1XS data will also permit geochemical studies of smaller scale features, such as the ejecta blankets and central peaks of large impact craters, and individual lava flows and pyroclastic deposits. These objectives all bear on important, and currently unresolved, questions in lunar science, including the structure and evolution of any primordial magma ocean, as revealed by vertical and lateral geochemical variations in the crust, and the composition of the lunar mantle, which will further constrain theories of the Moon's origin, thermal history and internal structure.