The Lyman-alpha forest absorption at z>2 can, with a sufficient density of background sightlines, be used to create 3D tomographic maps of large-scale structure. The Cosmic Lyman-Alpha Program for the Tomographic Reconstruction of Absorption Probes (CLAPTRAP) will be the first survey to attempt this technique. We aim to obtain spectra for a background grid of faint quasars and bright LBGs at 2<z<3 at a limiting apparent magnitude of g<24. These sources are separated by transverse comoving distances of ~4 cMpc enabling a 3D absorption map with ~4-5 cMpc spatial resolution to be reconstructed. In a recent paper, we have found that spectra with S/N ~4 per angstrom are sufficient to make excellent-quality maps that clearly trace the underlying dark-matter distribution at overdensities of order unity. Such spectra will require several hours' integration with moderate-resolution spectrographs on existing 8-10m telescopes. We aim to observe ~2500-3000 background sources over 1 sq deg of the COSMOS field with Ly-a forest coverage over 2.0<z<2.4, which would map out a total comoving volume of ~3x10^6 cMpc^3. The resulting tomographic maps will be the first 3D maps of large-scale structure at z>2, on ~Mpc scales. In conjunction with the rich multi-wavelength data from the COSMOS survey, these maps will facilitate the study of galaxies in the context of their large-scale environment, reveal the topology of the universe at high-redshifts, and allow the direct detection of galaxy protoclusters at the intersections of the cosmic web. The spectra will also be used to measure the small-scale Ly-a forest auto-correlation at <15 cMpc scales, which will place constraints on the properties of the IGM as well as cosmological parameters. In the near-future, Subaru PFS will be able to map out large areas of the high-redshift universe using this technique.