  We introduce a two-particle correlation function (2PCF) for the Milky Way,
constructed to probe spatial correlations in the orthogonal directions of the
stellar disk in the Galactic cylindrical coordinates of $R$, $\phi$, and $z$.
We use this new tool to probe the structure and dynamics of the Galaxy using
the carefully selected set of solar neighborhood stars ($d \lesssim 3\, \rm
kpc$) from Gaia Data Release 2 we previously employed for studies of axial
symmetry breaking in stellar number counts. We make additional, extensive
tests, comparing to reference numerical simulations, to ensure our control over
possibly confounding systematic effects. Supposing either axial or North-South
symmetry we divide this data set into two nominally symmetric sectors and
construct the 2PCF, in the manner of the Landy-Szalay estimator, from the Gaia
data. In so doing, working well away from the mid-plane region in which the
spiral arms appear, we have discovered distinct symmetry-breaking patterns in
the 2PCF in its orthogonal directions, thus establishing the existence of
correlations in stellar number counts at sub-kiloparsec length scales for the
very first time. Particularly, we observe extensive wave-like structures of
amplitude greatly in excess of what we would estimate if the system were in a
steady state. We study the variations in these patterns across the Galactic
disk, and with increasing $|z|$, and we show how our results complement other
observations of non-steady-state effects near the Sun, such as vertical
asymmetries in stellar number counts and the Gaia snail.
