  We present ALMA detections of the [CI] 1-0, CO J=3-2, and CO J=4-3 emission
lines, as well as the ALMA band 4 continuum for a compact star-forming galaxy
(cSFG) at z=2.225, 3D-HST GS30274. As is typical for cSFGs, this galaxy has a
stellar mass of $1.89 \pm 0.47\,\times 10^{11}\,\rm{M}_\odot$, with a star
formation rate of $214\pm44\,\rm{M}_\odot\,\rm{yr}^{-1}$ putting it on the
star-forming `main-sequence', but with an H-band effective radius of 2.5 kpc,
making it much smaller than the bulk of `main-sequence' star-forming galaxies.
The intensity ratio of the line detections yield an ISM density (~ 6 $\times
10^{4}\,\rm{cm}^{-3}$) and a UV-radiation field ( ~2 $\times 10^4\,\rm{G}_0$),
similar to the values in local starburst and ultra-luminous infrared galaxy
environments. A starburst phase is consistent with the short depletion times
($t_{\rm H2, dep} \leq 140$ Myr) we find using three different proxies for the
H2 mass ([CI], CO, dust mass). This depletion time is significantly shorter
than in more extended SFGs with similar stellar masses and SFRs. Moreover, the
gas fraction of 3D-HST GS30274 is smaller than typically found in extended
galaxies. We measure the CO and [CI] kinematics and find a FWHM line width of
~$750 \pm 41 $ km s$^{-1}$. The CO and [CI] FWHM are consistent with a
previously measured H$\alpha$ FWHM for this source. The line widths are
consistent with gravitational motions, suggesting we are seeing a compact
molecular gas reservoir. A previous merger event, as suggested by the
asymmetric light profile, may be responsible for the compact distribution of
gas and has triggered a central starburst event. This event gives rise to the
starburst-like ISM properties and short depletion times. The centrally located
and efficient star formation is quickly building up a dense core of stars,
responsible for the compact distribution of stellar light in 3D-HST GS30274.
