We have measured the charge asymmetry in like-sign dilepton yields from B(0)B*(0) meson decays using the CLEO detector at the Cornell Electron Storage Ring. We find a(0)(ll) identical with[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+ the absolute value of epsilon(B)(2)) = +0.0035+/-0.0103+/-0.0015 (uncertainties are statistical and systematic, respectively) for the CP impurity parameter, epsilon(B).