The recent synthesis of the superconductor LaFeAsO(0.89)F(0.11) with transition temperature T(c) approximately 26 K (refs 1-4) has been quickly followed by reports of even higher transition temperatures in related compounds: 41 K in CeFeAsO(0.84)F(0.16) (ref. 5), 43 K in SmFeAsO(0.9)F(0.1) (ref. 6), and 52 K in NdFeAsO(0.89)F(0.11) and PrFeAsO(0.89)F(0.11) (refs 7, 8). These discoveries have generated much interest 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 LaFeAsO(0.89)F(0.11) at high magnetic fields, up to 45 T, that show a remarkable enhancement of the upper critical field B(c2) compared to values expected from the slopes dB(c2)/dT approximately 2 T K(-1) near T(c), particularly at low temperatures where the deduced B(c2)(0) approximately 63-65 T exceeds the paramagnetic limit. We argue that oxypnictides represent a new class of high-field superconductors with B(c2) values surpassing those of Nb(3)Sn, MgB(2) and the Chevrel phases, and perhaps exceeding the 100 T magnetic field benchmark of the high-T(c) copper oxides.