  The fraction of stars forming in compact, gravitationally bound clusters (the
`cluster formation efficiency' or CFE) is an important quantity for deriving
the spatial clustering of stellar feedback and for tracing star formation using
stellar clusters across the Universe. Observations of clusters in nearby
galaxies have revealed a strong dependence of the CFE on the local gas density,
indicating that more stars form in star clusters when the star formation rate
surface density is higher. Previously, it has not been possible to test this
relation at very young ages and in clusters with individual stars resolved due
to the universally-low densities in the cluster-forming regions in the Local
Group. This has even led to the suggestion that the CFE increases with distance
from the Sun, which would suggest an observational bias. However, the Central
Molecular Zone of the Milky Way hosts clouds with densities that are orders of
magnitude higher than anywhere else in the Local Group. We report a measurement
of the CFE in the highest-density region in the Galaxy, Sgr~B2, based on ALMA
observations of high-mass young stellar objects. We find that over a third of
the stars ($37\pm7\%$) in Sgr~B2 are forming in bound clusters. This value is
consistent with the predictions of environmentally-dependent models for the CFE
and is inconsistent with a constant CFE in the Galaxy.
