  We observe coherent spin oscillations in an antiferromagnetic spin-1
Bose-Einstein condensate of sodium. The variation of the spin oscillations with
magnetic field shows a clear signature of nonlinearity, in agreement with
theory, which also predicts anharmonic oscillations near a critical magnetic
field. Measurements of the magnetic phase diagram agree with predictions made
in the approximation of a single spatial mode. The oscillation period yields
the best measurement to date of the sodium spin-dependent interaction
coefficient, determining that the difference between the sodium spin-dependent
s-wave scattering lengths $a_{f=2}-a_{f=0}$ is $2.47\pm0.27$ Bohr radii.
