We present the first observations of foreground Lyman-$alpha$ forest absorption from high-redshift galaxies, targeting 24 star-forming galaxies (SFGs) with $zsim 2.3-2.8$ 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 $2.20leq zleq 2.45$. 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 $simmathrm{Mpc}$ 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 $(100,h^{-1}mathrm{Mpc})^3$.
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