  We report discovery and spectroscopic follow-up of 21 astrometric binaries
containing solar-type stars and dark companions with masses near 1.4
$M_{\odot}$. The simplest interpretation is that the companions are dormant
neutron stars (NSs), though ultramassive white dwarfs (WDs) and tight WD+WD
binaries cannot be fully excluded. We selected targets from Gaia DR3
astrometric binary solutions in which the luminous star is on the main sequence
and the dynamically-implied mass of the unseen companion is (a) more than
$1.25\,M_{\odot}$ and (b) too high to be any non-degenerate star or close
binary. We obtained multi-epoch radial velocities (RVs) over a period of 700
days, spanning a majority of the orbits' dynamic range in RV. The RVs broadly
validate the astrometric solutions and significantly tighten constraints on
companion masses. Several systems have companion masses that are unambiguously
above the Chandrasekhar limit, while the rest have masses between 1.25 and 1.4
$M_{\odot}$. The orbits are significantly more eccentric at fixed period than
those of typical WD + MS binaries, perhaps due to natal kicks. Metal-poor stars
are overrepresented in the sample: 3 out of 21 objects (14%) have
[Fe/H]$\sim-1.5$ and are on halo orbits, compared to $\sim$0.5% of the parent
Gaia binary sample. The metal-poor stars are all strongly enhanced in lithium.
The formation history of these objects is puzzling: it is unclear both how the
binaries escaped a merger or dramatic orbital shrinkage when the NS progenitors
were red supergiants, and how they remained bound when the NSs formed. Gaia has
now discovered 3 black holes (BHs) in astrometric binaries with masses above 9
$M_{\odot}$, and 21 NSs with masses near $1.4\,M_{\odot}$. The lack of
intermediate-mass objects in this sample is striking, supporting the existence
of a BH/NS mass bimodality over 4 orders of magnitude in orbital period.
