  We have measured the parity-violating electroweak asymmetry in the elastic
scattering of polarized electrons from ^4He at an average scattering angle
<theta_lab> = 5.7 degrees and a four-momentum transfer Q^2 = 0.091 GeV^2. From
these data, for the first time, the strange electric form factor of the nucleon
G^s_E can be isolated. The measured asymmetry of A_PV = (6.72 +/- 0.84 (stat)
+/- 0.21 (syst) parts per million yields a value of G^s_E = -0.038 +/- 0.042
(stat) +/- 0.010 (syst), consistent with zero.
