  Observations at UV and optical wavelengths have revealed that galaxies at
z~1-4 host star-forming regions, dubbed "clumps", which are believed to form
due to the fragmentation of gravitationally unstable, gas-rich disks. However,
the detection of the parent molecular clouds that give birth to such clumps is
still possible only in a minority of galaxies, mostly at z~1. We investigated
the [CII] and dust morphology of a z~3.4 lensed galaxy hosting four clumps
detected in the UV continuum. We aimed to observe the [CII] emission of
individual clumps that, unlike the UV, is not affected by dust extinction, to
probe their nature and cold gas content. We conducted ALMA observations probing
scales down to ~300 pc and detected three [CII] clumps. One (dubbed "NE")
coincides with the brightest UV clump, while the other two ("SW" and "C") are
not detected in the UV continuum. We do not detect the dust continuum. We
converted the [CII] luminosity of individual clumps into molecular gas mass and
found Mmol~10^8 Msun. By complementing it with the star formation rate (SFR)
estimate from the UV continuum, we estimated the gas depletion time (tdep) of
clumps and investigated their location in the Schmidt-Kennicutt plane. While
the NE clump has a short tdep=0.16 Gyr, comparable with high-redshift
starbursts, the SW and C clumps instead have longer tdep>0.65 Gyr and are
likely probing the initial phases of star formation. The lack of dust continuum
detection is consistent with the blue UV continuum slope estimated for this
galaxy (beta~-2.5) and it indicates that dust inhomogeneities do not
significantly affect the detection of UV clumps in this target. We pushed the
observation of the cold gas content of individual clumps up to z~3.4 and showed
that the [C II] line emission is a promising tracer of molecular clouds at high
redshift, allowing the detection of clumps with a large range of depletion
times.
