  We have measured the charge asymmetry in like-sign dilepton yields from B^0
B^0-bar meson decays using the CLEO detector at the Cornell Electron Storage
Ring. We find a_ll = [N(l+l+) - N(l-l-)]/[N(l+l+) + N[l-l-)] = +0.013 +/- 0.050
+/- 0.005 . We combine this result with a previous, independent measurement and
obtain Re(epsilon_B)/(1+|epsilon_B|^2) = +0.0035 +/- 0.0103 +/- 0.0015
(uncertainties are statistical and systematic, respectively) for the CP
impurity parameter, epsilon_B.
