  Chemically tagging groups of stars born in the same birth cluster is a major
goal of spectroscopic surveys. To investigate the feasibility of such strong
chemical tagging, we perform a blind chemical tagging experiment on abundances
measured from APOGEE survey spectra. We apply a density-based clustering
algorithm to the eight dimensional chemical space defined by [Mg/Fe], [Al/Fe],
[Si/Fe], [K/Fe], [Ti/Fe], [Mn/Fe], [Fe/H], and [Ni/Fe], abundances ratios which
together span multiple nucleosynthetic channels. In a high quality sample of
182,538 giant stars, we detect twenty-one candidate clusters with more than
fifteen members. Our candidate clusters are more chemically homogeneous than a
population of non-member stars with similar [Mg/Fe] and [Fe/H], even in
abundances not used for tagging. Group members are consistent with having the
same age and fall along a single stellar-population track in logg vs. Teff
space. Each group's members are distributed over multiple kpc, and the spread
in their radial and azimuthal actions increases with age. We qualitatively
reproduce this increase using N-body simulations of cluster dissolution in
Galactic potentials that include transient winding spiral arms. Observing our
candidate birth clusters with high-resolution spectroscopy in other wavebands
to investigate their chemical homogeneity in other nucleosynthetic groups will
be essential to confirming the efficacy of strong chemical tagging. Our
initially spatially-compact but now widely dispersed candidate clusters will
provide novel limits on chemical evolution and orbital diffusion in the
Galactic disc, and constraints on star formation in loosely-bound groups.

Astrophysics of Galaxies;Solar and Stellar Astrophysics