Step 1Spoon cheese, a generous tablespoon at a time, into nonstick skillet. You should be able to fit 3 or 4 tablespoons into skillet. Spread cheese into thin rounds. Heat over medium heat until cheese melts and lightly browns on bottom, about 2 minutes. Turn and brown other side. Remove to paper towel to cool.
Step 2Pound chicken breasts to flatten slightly. Remove skin and season with salt and pepper. Spray or lightly brush a nonstick skillet with olive oil. Add butter and melt over medium heat. Add chicken breasts and saute until browned, about 5 minutes, then turn and brown second side. Remove from skillet and keep warm.
Step 3Add garlic and artichoke hearts to skillet, and saute 3 to 4 minutes. Stir in capers and olives and saute 1 to 2 minutes more. Stir in broth and heat to simmer. Blend together flour and water until smooth, and stir into simmering sauce. Heat and stir until slightly thickened, about 1 minute. Stir in lemon juice and tarragon. Add chicken breasts to sauce, spooning sauce over top of chicken. Simmer a few minutes for flavors to blend.
Step 4To serve, slice chicken breast on the diagonal. Arrange on plate and spoon sauce over chicken. Break frico over top of chicken.