  We present the first observations of foreground Lyman-$\alpha$ forest
absorption from high-redshift galaxies, targeting 24 star-forming galaxies
(SFGs) with $z\sim 2.3-2.8$ within a $5' \times 15'$ region of the COSMOS
field. The transverse sightline separation is $\sim 2\,h^{-1}\mathrm{Mpc}$
comoving, allowing us to create a tomographic reconstruction of the 3D
Ly$\alpha$ forest absorption field over the redshift range $2.20\leq z\leq
2.45$. The resulting map covers $6\,h^{-1}\mathrm{Mpc} \times
14\,h^{-1}\mathrm{Mpc}$ in the transverse plane and $230\,h^{-1}\mathrm{Mpc}$
along the line-of-sight with a spatial resolution of $\approx
3.5\,h^{-1}\mathrm{Mpc}$, and is the first high-fidelity map of large-scale
structure on $\sim\mathrm{Mpc}$ scales at $z>2$. Our map reveals significant
structures with $\gtrsim 10\,h^{-1}\mathrm{Mpc}$ extent, including several
spanning the entire transverse breadth, providing qualitative evidence for the
filamentary structures predicted to exist in the high-redshift cosmic web.
Simulated reconstructions with the same sightline sampling, spectral
resolution, and signal-to-noise ratio recover the salient structures present in
the underlying 3D absorption fields. Using data from other surveys, we
identified 18 galaxies with known redshifts coeval with our map volume enabling
a direct comparison to our tomographic map. This shows that galaxies
preferentially occupy high-density regions, in qualitative agreement with the
same comparison applied to simulations. Our results establishes the feasibility
of the CLAMATO survey, which aims to obtain Ly$\alpha$ forest spectra for $\sim
1000$ SFGs over $\sim 1 \,\mathrm{deg}^2$ of the COSMOS field, in order to map
out IGM large-scale structure at $\langle z \rangle \sim 2.3$ over a large
volume $(100\,h^{-1}\mathrm{Mpc})^3$.
