  Ongoing surveys are in the process of measuring the chemical abundances in
large numbers of stars, with the ultimate goal of reconstructing the formation
history of the Milky Way using abundances as tracers. However, interpretation
of these data requires that we understand the relationship between stellar
distributions in chemical and physical space, i.e., how similar in chemical
abundance do we expect a pair of stars to be as a function of the distance
between their formation sites. We investigate this question by simulating the
gravitational collapse of a turbulent molecular cloud extracted from a
galaxy-scale simulation, seeded with chemical inhomogeneities with different
initial spatial scales. We follow the collapse from galactic scales down to
resolutions scales of $\approx 10^{-3}$ pc, and find that, during this process,
turbulence mixes the metal patterns, reducing the abundance scatter initially
present in the gas by an amount that depends on the initial scale of
inhomogeneity of each metal field. However, we find that regardless of the
initial spatial structure of the metals at the onset of collapse, the final
stellar abundances are highly correlated on distances below a few pc, and
nearly uncorrelated on larger distances. Consequently, the star formation
process defines a natural size scale of $\sim 1$ pc for chemically-homogenous
star clusters, suggesting that any clusters identified as homogenous in
chemical space must have formed within $\sim 1$ pc of one another. However, in
order to distinguish different star clusters in chemical space, observations
across multiple elements will be required, and the elements that are likely to
be most efficient at separating distinct clusters in chemical space are those
whose correlation length in the ISM is of order tens of pc, comparable to the
sizes of individual molecular clouds.
