  From an observational point of view, the role of magnetic fields in star
formation remains unclear, and two main theoretical scenarios have been
proposed so far to regulate the star-formation processes. The first model
assumes that turbulence in star-forming clumps plays a crucial role, and
especially that protostellar outflow-driven turbulence is crucial to support
cluster-forming clumps; while the second scenario is based on the consideration
of a magnetically-supported clump. Previous studies of the NGC 2264-C
protocluster indicate that, in addition to thermal pressure, some extra support
might effectively act against the gravitational collapse of this
cluster-forming clump. We previously showed that this extra support is not due
to the numerous protostellar outflows, nor the enhanced turbulence in this
protocluster. Here we present the results of the first polarimetric campaign
dedicated to quantifying the magnetic support at work in the NGC 2264-C clump.
Our Zeeman observations of the CN(1-0) hyperfine lines provide an upper limit
to the magnetic field strength B_los \leq0.6 mG in the protocluster (projected
along the line of sight). While these results do not provide sufficiently tight
constraints to fully quantify the magnetic support at work in NGC 2264-C, they
suggest that, within the uncertainties, the core could be either magnetically
super or sub-critical, with the former being more likely.
