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.