Context. The importance of magnetic fields at the onset of star formation related to the early fragmentation and collapse processes is largely unexplored today. Aims. We want to understand the magnetic field properties at the earliest evolutionary stages of high-mass star formation. Methods. The Atacama Large Millimeter Array is used at 1.3 mm wavelength in full polarization mode to study the polarized emission, and, using this, the magnetic field morphologies and strengths of the high-mass starless region IRDC 18310-4. Results. Polarized emission is clearly detected in four sub-cores of the region; in general it shows a smooth distribution, also along elongated cores. Estimating the magnetic field strength via the Davis-Chandrasekhar-Fermi method and following a structure function analysis, we find comparably large magnetic field strengths between ~0.3–5.3 mG. Comparing the data to spectral line observations, the turbulent-to-magnetic energy ratio is low, indicating that turbulence does not significantly contribute to the stability of the gas clump. A mass-to-flux ratio around the critical value 1.0 – depending on column density – indicates that the region starts to collapse, which is consistent with the previous spectral line analysis of the region. Conclusions. While this high-mass region is collapsing and thus at the verge of star formation, the high magnetic field values and the smooth spatial structure indicate that the magnetic field is important for the fragmentation and collapse process. This single case study can only be the starting point for larger sample studies of magnetic fields at the onset of star formation.