Melt margarine in a large, non-stick fry pan over medium-high heat.
Brown chicken meat side down, about 3 minutes. When brown, turn chicken pieces over.
Stir minced onion into broth and pour over chicken.
Sprinkle tarragon and parsley over.
Cover pan with tight-fitting lid and turn to simmer.
Cook for 15 minutes. Test for doneness by cutting through thickest part of largest piece of chicken. If any pink remains, cover and cook additional 5 minutes and retest.
When done, transfer chicken to serving platter and tent with foil to keep warm while making sauce.
Combine cornstarch and water, stirring till smooth.
Turn heat to high and reduce tarragon broth in pan by half.
Whisk in cornstarch and continue cooking till slightly thickened.
Pour over chicken and serve.