Clean chicken. In 12" skillet, over medium heat, melt butter. When bubbly, add chicken pieces, skin side down. Saute 20 minutes till deep golden-brown color. Shake pan now and then so chicken doesn't stick to the bottom.
Turn chicken pieces. Sprinke half the tarragon into the butter. Saute chicken 20 minutes more. Remove chicken to large plate or platter. Pour grease out of skillet into a cup.
Remove root end of scallions. Slice scallions lengthwise, then cut them up in thin slivers crosswise. Add scallions and other half of tarragon to skillet. Return 1 tablespoon of grease from cup to skillet.
Cook, stirring, 1 minute over medium heat. Pour in chicken broth. Cook and scrape the bottom of skillet with wooden spoon to swirl all collected bits into broth. Let bubble 1-2 minutes. Pour all over chicken