We report on the single crystal growth of the single-layer perovskite cobaltate LaSrCoO₄ that was grown by the optical floating zone method using high oxygen pressures. Phase purity and single crystallinity were confirmed by X-ray diffraction techniques. The pure Co³⁺ oxidation state was confirmed by X-ray absorbtion spectroscopy measurements. A transition to a spin glass state is observed at ∼7 K in magnetic susceptibility and specific heat measurements.