We report the discovery and spectroscopic confirmation of a very large star-forming Lyman Break galaxy, G6025, at z_spec=3.721+/-0.003. In the rest-frame ~2100A, G6025 subtends ~24 kpc in physical extent when measured from the 1.5-sigma isophote, in agreement with the parametric size measurements which yield the half-light radius of 4.9+/-0.5 kpc and the semi-major axis of 12.5+/-0.1 kpc. G6025 is also very UV-luminous (~5L*(z~4}) and young (~140+/-60 Myr). Despite its unusual size and luminosity, the stellar population parameters and dust reddening (M_star~M*(z~4)$, and E(B-V)=0.18+/-0.05) estimated from the integrated light, are similar to those of smaller galaxies at comparable redshifts. The ground-based morphology and spectroscopy show two dominant components, both located off-center, embedded in more diffuse emission. We speculate that G6025 may be a scaled-up version of chain galaxies seen in deep HST imaging, or alternatively, a nearly equal-mass merger involving two super-L* galaxies in its early stage. G6025 lies close to but not within a known massive protocluster at z=3.78. We find four companions within 6 Mpc from G6025, two of which lie within 1.6 Mpc. While the limited sensitivity of the existing spectroscopy does not allow us to robustly characterize the local environment of G6025, it likely resides in a locally overdense environment. The luminosity, size, and youth of G6025 make it uniquely suited to study the early formation of massive galaxies in the universe.
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