Lightly pound chicken breasts to even thickness. Dust chicken with flour, and add salt and pepper to your taste.
In a heavy skillet, heat 1 tablespoon olive oil over medium heat. Place chicken in pan, brown on both sides, and cook through; this will take about 8 to 10 minutes. Remove from pan, and set aside.
Add remaining 1 tablespoon olive oil, and saute onions and mushrooms over medium heat for 3 to 5 minutes.
Add beef broth, lemon juice, tarragon, and artichoke hearts to the pan: heat for 2 to 3 minutes, stirring gently. Stir in brandy, and simmer for an additional 2 to 3 minutes. Return chicken to the pan, and heat through.
