Heat 4 tablespoons oil in heavy large skillet over medium heat.
Add onion, anchovies and garlic. Sauté until onion is tender but not brown, mashing anchovies with fork, about 3 minutes.
Increase heat to medium-high. Add chicken livers and sauté until brown, about 4 minutes.
Add wine and cook until most of liquid evaporates, about 3 minutes.
Add chicken broth and sage. Simmer until chicken livers are cooked through and liquid is reduced by half, breaking up livers with fork, about 10 minutes. Cool slightly.
Transfer mixture to processor. Using short bursts, process just until livers are coarsely pureed. Mix in lemon peel. Season to taste with salt and pepper.