The conversion of gas into stars is a fundamental process in astrophysics and cosmology. Stars are known to form from the gravitational collapse of dense clumps in interstellar molecular clouds, and it has been proposed that the resulting star formation rate is proportional to either the amount of mass above a threshold gas surface density, or the gas volume density. These star formation prescriptions appear to hold in nearby molecular clouds in our MilkyWay Galaxy's disc as well as in distant galaxies where the star formation rates are often much larger. The inner 500 pc of our Galaxy, the Central Molecular Zone (CMZ), contains the largest concentration of dense, high-surface density molecular gas in the Milky Way, providing an environment where the validity of star formation prescriptions can be tested. Here, we show that by several measures, the current star formation rate in the CMZ is an order-of-magnitude lower than the rates predicted by the currently accepted prescriptions. In particular, the region 1° <l <3.°5, b <0.°5 contains ~107 M of dense (> several 103 cm-3) molecular gas - enough to form 1000 Orion-like clusters - but the present-day star formation rate within this gas is only equivalent to that in Orion. In addition to density, another property of molecular clouds must be included in the star formation prescription to predict the star formation rate in a given mass of molecular gas. We discuss which physical mechanisms might be responsible for suppressing star formation in the CMZ. © 2012 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.