  Massive galaxies in the early Universe have been shown to be forming stars at
surprisingly high rates. Prominent examples are dust-obscured galaxies which
are luminous when observed at sub-millimeter (sub-mm) wavelengths and which may
be forming stars at rates upto 1,000Mo/yr. These intense bursts of star
formation are believed to be driven by mergers between gas rich galaxies.
However, probing the properties of individual star-forming regions within these
galaxies is beyond the spatial resolution and sensitivity of even the largest
telescopes at present. Here, we report observations of the sub-mm galaxy
SMMJ2135-0102 at redshift z=2.3259 which has been gravitationally magnified by
a factor of 32 by a massive foreground galaxy cluster lens. This cosmic
magnification, when combined with high-resolution sub-mm imaging, resolves the
star-forming regions at a linear scale of just ~100 parsecs. We find that the
luminosity densities of these star-forming regions are comparable to the dense
cores of giant molecular clouds in the local Universe, but they are ~100x
larger and 10^7 times more luminous. Although vigorously star-forming, the
underlying physics of the star formation processes at z~2 appears to be similar
to that seen in local galaxies even though the energetics are unlike anything
found in the present-day Universe.
