In large skillet cook prosciutto in the 2 teaspoons hot oil over medium-high heat 2 minutes or until crisp. Remove. Sprinkle chicken with salt and pepper. Cook in same skillet 8-10 minutes or until browned, turning once. Transfer to a bowl; set aside.
Add remaining olive oil and artichokes to skillet. Cook and stir 3 minutes until golden brown. Transfer to the bowl with chicken. Add mushrooms to skillet. Cook 3 minutes, stirring up browned bits, until golden. Stir in garlic and tarragon; cook 1 minute.
In second bowl whisk together flour, broth, and vinegar. Remove skillet from heat. Add broth mixture. Add chicken and artichokes. Return to heat. Bring to boiling; reduce heat. Simmer, uncovered, until thickened. Top with prosciutto and tarragon.