  Recent experiments indicate that static stripe-like charge order is generic
to the hole-doped copper oxide superconductors and competes with
superconductivity. Here we show that a similar type of charge order is present
in La$_{5/3}$Sr$_{1/3}$CoO$_4$, an insulating analogue of the copper oxide
superconductors containing cobalt in place of copper. The stripe phase we have
detected is accompanied by short-range, quasi-one-dimensional,
antiferromagnetic order, and provides a natural explanation for the distinctive
hourglass shape of the magnetic spectrum previously observed in neutron
scattering measurements of La$_{5/3}$Sr$_{1/3}$CoO$_4$ and many hole-doped
copper oxide superconductors. The results establish a solid empirical basis for
theories of the hourglass spectrum built on short-range, quasi-static, stripe
correlations.
