Faint star-forming galaxies at z~2-3 can be used as alternative background sources to probe the Ly{alpha} forest in addition to quasars, yielding high sightline densities that enable 3D tomographic reconstruction of the foreground absorption field. Here, we present the first data release from the COSMOS Ly{alpha} Mapping And Tomography Observations (CLAMATO) Survey, which was conducted with the LRIS spectrograph on the Keck I telescope. Over an observational footprint of 0.157deg^2^ within the COSMOS field, we used 240 galaxies and quasars at 2.17<z<3.00, with a mean comoving transverse separation of 2.37h^-1^Mpc, as background sources probing the foreground Ly{alpha} forest absorption at 2.05<z<2.55. The Ly{alpha} forest data was then used to create a Wiener-filtered tomographic reconstruction over a comoving volume of 3.15x10^5^h^-3^Mpc^3^ with an effective smoothing scale of 2.5h^-1^Mpc. In addition to traditional figures, this map is also presented as a virtual-reality visualization and manipulable interactive figure. We see large overdensities and underdensities that visually agree with the distribution of coeval galaxies from spectroscopic redshift surveys in the same field, including overdensities associated with several recently discovered galaxy protoclusters in the volume. Quantitatively, the map signal-to-noise is S/N^wiener^~3.4 over a 3h^-1^Mpc top-hat kernel based on the variances estimated from the Wiener filter. This data release includes the redshift catalog, reduced spectra, extracted Ly{alpha} forest pixel data, and reconstructed tomographic map of the absorption.