NMR measurements were performed on single-crystalline samples of the one-dimensional Heisenberg antiferromagnet ͑1D HAF͒ LiCuVO 4 . We investigated 7 Li and 51 V NMR spectra, deduced the respective lineshifts K͑T͒, spin-lattice relaxation rates 1 / T 1 , and spin-spin relaxation rates 1 / T 2 and 1 / T 2G . The results are compared to theoretical predictions for the relaxation rates 1 / T 1 ͑T͒ and 1 / T 2G ͑T͒ deduced from the dynamic susceptibility ͑q , ͒ of a 1D HAF spin chain as proposed by Sachdev ͓Phys. Rev. B 50, 13006 ͑1994͔͒. We document a correspondence between the anisotropic relaxation rates derived from electron paramagnetic resonance linewidth ⌬H͑T͒ and nuclear magnetic resonance 1 / T 1 ͑T͒, respectively, the former being well described in the framework of symmetric anisotropic exchange interactions for LiCuVO 4 by Krug von Nidda et al. ͓Phys. Rev. B 65, 134445 ͑2002͔͒.