We present the first data release of the Radial Velocity Experiment (RAVE), an ambitious spectroscopic survey to measure radial velocities and stellar atmosphere parameters (temperature, metallicity, and surface gravity) of up to one million stars using the Six Degree Field multiobject spectrograph on the 1.2 m UK Schmidt Telescope of the Anglo-Australian Observatory. The RAVE program started in 2003, obtaining medium-resolution spectra (median R = 7500) in the Ca-triplet region (8410-8795 Å) for southern hemisphere stars drawn from the Tycho-2 and SuperCOSMOS catalogs, in the magnitude range 9 < I < 12. The first data release is described in this paper and contains radial velocities for 24,748 individual stars (25,274 measurements when including reobservations). Those data were obtained on 67 nights between 2003 April 11 and 2004 April 3. The total sky coverage within this data release is ~4760 deg2. The average signal-to-noise ratio of the observed spectra is 29.5, and 80% of the radial velocities have uncertainties better than 3.4 km s-1. Combining internal errors and zero-point errors, the mode is found to be 2 km s-1. Repeat observations are used to assess the stability of our radial velocity solution, resulting in a variance of 2.8 km s-1. We demonstrate that the radial velocities derived for the first data set do not show any systematic trend with color or signal-to-noise ratio. The RAVE radial velocities are complemented in the data release with proper motions from Starnet 2.0, Tycho-2, and SuperCOSMOS, in addition to photometric data from the major optical and infrared catalogs (Tycho-2, USNO-B, DENIS, and the Two Micron All Sky Survey). The data release can be accessed via the RAVE Web site.