  The magnetism of Sr$_2$F$_2$Fe$_2$OS$_2$ was examined through neutron powder
diffraction and thermodynamic and transport measurements. Quasi-two-dimensional
magnetic order develops below $T_N$ = 106(2) K with an in-plane correlation
length exceeding 310 \AA\ and an out-of-plane correlation length of just 17(3)
\AA. The data are consistent with a two-k structure with $k_1$ = (1/2, 0, 1/2)
and $k_2$ = (0, 1/2, 1/2) and an ordered moment of 3.3(1) $\mu_B$ oriented
along the in-plane components of k. This structure is composed of orthogonal
AFM chains intersecting at super-exchange mediating O sites. Density Functional
Theory (DFT) also points to this structure and a narrower Fe 3d band than for
the iron pnictides from which electronic correlations produce a Mott insulator.
