We report giant values of saturation magnetoresistance in sputtered antiferromagnetic Co/Cu multilayers containing thin Co and Cu layers 8-10 Å thick. We discuss the key importance of the buffer layer in controlling the growth of flat Co and Cu layers. As shown by cross-section transmission electron microscopy high-quality structures are found for growth on Fe buffer layers. Such structures display saturation magnetoresistance at 300 K of more than 65% with saturation fields of ≃10 kOe. These values are several times larger than previously found for any magnetic material at room temperature.