The recent synthesis of the superconductor LaFeAsO0.89F0.11 with transition temperature Tc 26 K (refs 1–4) has been quickly followed by reports of even higher transition temperatures in related compounds: 41 K in CeFeAsO0.84F0.16 (ref. 5), 43 K in SmFeAsO0.9F0.1 (ref. 6), and 52 K in NdFeAsO0.89F0.11 and PrFeAsO0.89F0.11 (refs 7, 8). These discoveries have generated much interest9, 10 in the mechanisms and manifestations of unconventional superconductivity in the family of doped quaternary layered oxypnictides LnOTMPn (Ln: La, Pr, Ce, Sm; TM: Mn, Fe, Co, Ni; Pn: P, As), because many features of these materials set them apart from other known superconductors. Here we report resistance measurements of LaFeAsO0.89F0.11 at high magnetic fields, up to 45 T, that show a remarkable enhancement of the upper critical field Bc2 compared to values expected from the slopes dBc2/dT 2 T K-1 near Tc, particularly at low temperatures where the deduced Bc2(0) 63–65 T exceeds the paramagnetic limit. We argue that oxypnictides represent a new class of high-field superconductors with Bc2 values surpassing those of Nb3Sn, MgB2 and the Chevrel phases, and perhaps exceeding the 100 T magnetic field benchmark of the high-Tc copper oxides.