Pt/Co/Pt sandwich films grown on single-crystal MgO substrates have been found to show an anomalous enhancement of the in-plane magnetic anisotropy for ultrathin Co layers below 1 nm. The in-plane sixfold anisotropy of (111)-oriented films yielded a maximum value of about - 1 x 10(6) erg/cm(3) for 1 nm thickness, which is two orders of magnitude larger than that of fee Co. For samples with (100) orientation, in-plane fourfold anisotropy increases with decreasing Co layer thickness, showing a maximum value of + 1.9 x 10(6) erg/cm(3) at a thickness of one monolayer.