Techniques that use quantum interference effects are being attively investigated to manipulate the optical properties of quantum systems(1). One such example is electromagnetically induced transparency, a quantum effect that permits the propagation of light pulses through an otherwise opaque medium(2-5). Here we report an experimental demonstration of electromagnetically induced transparency in an ultracold gas of sodium atoms, in which the optical pulses propagate at twenty million times slower than the speed of light in a vacuum. The gas is cooled to nanokelvin temperatures by laser and evaporative cooling(6-10) The quantum interference controlling the optical properties of the medium is set up by a ＇coupling＇ laser beam propagating at a right angle to the pulsed ＇probe＇ beam. At nanokelvin temperatures, the variation of refractive index with probe frequency can be made very steep. In conjunction with the high atomic density, this results in the exceptionally low light speeds observed. By cooling the cloud below the transition temperature for Bose-Einstein condensation(11-13) (causing a macroscopic population of alkali atoms in the quantum ground state of the confining potential), we observe even lower pulse propagation velocities (17 m s(-1)) owing to the increased atom density. We report an inferred nonlinear refractive index of 0.18 cm(2) W-1 and find that the system shows exceptionally large optical nonlinearities, which are of potential fundamental and technological interest for quantum optics.