We report, for magnetic fields of 0, 8.8, and 14.8 Tesla, measurements of the temperature dependent ^{63}Cu NMR spin lattice relaxation rate for near optimally doped YBa_2Cu_3O_{7-delta}, near and above T_c. In sharp contrast with previous work we find no magnetic field dependence. We discuss experimental issues arising in measurements of this required precision, and implications of the experiment regarding issues including the spin or pseudo gap.