Sprinkle chicken with salt and pepper and dredge in flour. Set aside remaining flour.

Heat 3 tablespoons of butter over medium heat in large skillet and brown chicken on both sides. Remove chicken and keep warm.

Saute onion in same skillet until it begins to become clear.

Add wine and cook until liquid is almost evaporated, stirring to loosen browned bits (deglaze) on bottom of skillet. Watch closely- this happens fast!

Reduce heat to medium-low and stir in reserved flour until it becomes a thick paste.

Add tarragon, chicken broth and the cooked chicken. Cover and cook until tender.

Place chicken on a warm platter.

Add remaining butter and heavy cream to the liquid that is in the skillet and heat through.

Pour sauce over the chicken and garnish with a little more tarragon or some chopped fresh parsley or green onion if desired.