We report on a precision measurement of the neutron spin structure fun
ction g(l)(n) using deep inelastic scattering of polarized electrons b
y polarized He-3. For the kinematic range 0.014 < x < 0.7 and 1 < Q(2)
< 17 (GeV/c)(2), we obtain integral(0.014)(0.7) g(l)(n)(x)dx = -0.036
+/- 0.004(stat) +/- 0.005(syst) at an average Q(2) = 5 (GeV/c)(2). We
find relatively large negative values for g(l)(n) at low x. The resul
ts call into question the usual Regge theory method for extrapolating
to x = 0 to find the full neutron integral integral(0)(1) g(l)(n)(x)dx
, needed for testing the quark-parton model and QCD sum rules.