  We have prepared a series of polycrystalline samples
La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$} with $0 < \delta \le 0.21$ and
characterized their oxygen content, crystal structure, and magnetic properties.
While the fully oxygenated samples are good ferromagnets, samples with larger
$\delta$ values display increasingly broad magnetic transitions. The saturation
magnetization at 5 K falls rapidly as $\delta$ increases. First principles
electronic structure calculations provide insights into the magnetic behavior
of the fully oxygenated compound, and the manner in which ferromagnetic
ordering is affected by increasing oxygen non-stoichiometry.
