Ultrathin Co films have been electrodeposited on Cu(001) from an aqueous Na₂SO₄/CoSO₄ electrolyte under cleanliness conditions equivalent to ultrahigh vacuum of 5 x 10⁻¹⁰ mbar. Films thicker than 1.5 ML show in-plane magnetization and square hysteresis loops. The saturation magnetization increases linearly with film thickness. The magnetization vanishes below 1.5 ML in agreement with molecular-beam epitaxy (MBE) films at 300 K. The coercivity varies approximately linearly with film thickness and is ten times larger than usually observed in MBE-grown Co. "Magnetically dead" layers have not been found.