  We report ^{115}In and ^{59}Co Nuclear Magnetic Resonance (NMR) measurements
in the heavy fermion superconductor CeCoIn_5 above and below T_c. The hyperfine
couplings of the In and Co are anisotropic and exhibit dramatic changes below
50K due to changes in the crystal field level populations of the Ce ions. Below
T_c the spin susceptibility is suppressed, indicating singlet pairing.
