  We conduct a line-by-line differential analysis of a sample of 125 co-moving
pairs of stars (dwarfs and subgiants near solar metallicity). We obtain high
precision stellar parameters with average uncertainties in effective
temperature, surface gravity and metallicity of 16.5 K, 0.033 dex and 0.014
dex, respectively. We classify the co-moving pairs of stars into two groups,
chemically homogeneous (conatal; |Delta[Fe/H]| $\le$ 0.04 dex) and
inhomogeneous (non-conatal), and examine the fraction of chemically homogeneous
pairs as a function of separation and effective temperature. The four main
conclusions from this study are: (1) A spatial separation of \ds = 10$^6$ AU is
an approximate boundary between homogeneous and inhomogeneous pairs of stars,
and we restrict our conclusions to only consider the 91 pairs with \ds $\le$
10$^6$ AU; (2) There is no trend between velocity separation and the fraction
of chemically homogeneous pairs in the range \dv $\le$ 4 \kms; (3) We confirm
that the fraction of chemically inhomogeneous pairs increases with increasing
\teff\ and the trend matches a toy model of that expected from planet
ingestion; (4) Atomic diffusion is not the main cause of the chemical
inhomogeneity. A major outcome from this study is a sample of 56 bright
co-moving pairs of stars with chemical abundance differences $\leq$ 0.02 dex
(5\%) which is a level of chemical homogeneity comparable to that of the Hyades
open cluster. These important objects can be used, in conjunction with star
clusters and the \gaia\ ``benchmark'' stars, to calibrate stellar abundances
from large-scale spectroscopic surveys.
