We have performed 75As nuclear magnetic resonance measurements on aligned powders of the new LaFeAsO0.9F0.1 superconductor. In the normal state, we find a strong temperature dependence of the spin shift and Korringa behavior of the spin lattice relaxation rate. In the superconducting state, we find evidence for line nodes in the superconducting gap and spin-singlet pairing. Our measurements reveal a strong anisotropy of the spin lattice relaxation rate, which suggests that superconducting vortices contribute to the relaxation rate when the field is parallel to the c axis but not for the perpendicular direction.