  We report measurements on Ti$_4$MnBi$_2$, where a crystal structure involving
linear chains of Mn ions suggests one-dimensional magnetic character. The
electrical resistivity is metallic, consistent with the results of electronic
structure calculations that find a robust Fermi surface albeit with moderate
electronic correlations. Curie-Weiss fit to the magnetic susceptibility finds
that the Mn moments are in the low-spin $S = 1/2$ configuration. Neutron
diffraction measurements detect weak antiferromagnetic order within the Mn
chains, with further evidence for the small staggered moment coming from the
entropy associated with the ordering peak in the specific heat as well as from
the results of spin-polarized electronic structure calculations. The
antiferromagnetic moments are apparently associated with the $d_{x^{2}-y^{2}}$
and $d_{xy}$ orbitals of Mn while the remaining Mn orbitals are delocalized.
Strong quantum fluctuations, possibly related to an electronic instability that
forms the Mn moment or to the one-dimensional character of Ti$_4$MnBi$_2$,
nearly overcome magnetic order.
