From 1310.6 x 10(6) J/psi and 448.1 x 10(6) psi (3686) events collected with the BESIII experiment, we report the first observation of Sigma(+) and (Sigma) over bar (-) spin polarization in e(+)e(-) -> J/psipsi(3686) -> Sigma(+)(Sigma) over bar (-) decays. The relative phases of the form factors Delta Phi have been measured to be (-15.5 +/- 0.7 +/- 0.5)degrees and (21.7 +/- 4.0 +/- 0.8)degrees with J/psi and psi(3686) data, respectively. The nonzero value of Delta Phi allows for a direct and simultaneous measurement of the decay asymmetry parameters of Sigma(+)-> p pi(0) (alpha(0) = -0.998 +/- 0.037 +/- 0.009) and (Sigma) over bar (-)-> (p) over bar pi(0) ((alpha) over bar (0) = 0.990 +/- 0.037 +/- 0.011), the latter value being determined for the first time. The average decay asymmetry, (alpha(0 )- (alpha) over bar (0))/2, is calculated to be -0.994 +/- 0.004 +/- 0.002. The CP asymmetry A(CP,Sigma) = (alpha(0) + (alpha) over bar (0))/(alpha(0) - (alpha) over bar (0)) = -0.004 +/- 0.037 +/- 0.010 is extracted for the first time, and is found to be consistent with CP conservation.