In medium saucepan melt butter over medium heat. Add flour and cook for several minutes. Add garlic, cream cheese, milk, chicken broth and salt and pepper to taste. For extra flavor, add 1/4 cup of the artichoke marinade. Cook over med-low heat until mixture thickens.
In 8x12" casserole dish, spread drained artichokes on bottom. Top with chicken breasts and pour cream sauce over. Crush Ritz crackers and spread on top. Bake in a 350 degree oven for 40 minutes.