Recent studies of galaxies ~2-3 Gyr after the Big Bang have revealed large, turbulent rotating systems. The existence of well-ordered rotation in galaxies during this peak epoch of cosmic star formation may suggest that gas accretion through cold streams is likely to be the dominant mode by which most star-forming galaxies at high redshift since major mergers can completely disrupt the observed velocity fields. However poor spatial resolution and sensitivity have hampered this interpretation, limiting the study to the largest and most luminous galaxies, which may have fundamentally different modes of assembly than more typical star forming galaxies. Here we report observations of a typical star forming galaxy at z=3.07 with a linear resolution of ~100 parsec. This spatial sampling is made possible by the combination of gravitational lensing and laser guide star adaptive optics. We find a well-ordered compact source in which molecular gas is being converted efficiently into stars, likely assembling a spheroidal bulge and disk similar to those seen in spiral galaxies at the present day.
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