Heat oven to 475. Set a large cast-iron skillet over high heat until very hot. Season chicken pieces with salt. Reduce heat of skilled to medium high and add oil. Add chicken skin side down, 1 tablespoon butter, garlic and thyme and cook until skin is browned about 5-7 minutes.
Turn chicken skin side up and transfer skillet to lowest rack. Roast chicken until breast juices run clear about 10-15 minutes. Transfer breasts to platter. Return skillet to oven and cook until leg juices run clear - another 5-10 minutes. Transfer legs to platter and discard garlic and thyme.
Pour off fat in skillet. Set skillet over high heat. Add vinegar and simmer scraping up brown bits about 1 minutes. Add tomatoes and cook, stirring occasionally, until liquid is reduced by half, about 5 minutes. Remove skillet from heat and add remaining butter and stir until it melts.
Spoon sauce over chicken ,sprinkle with salt/pepper, garnish tarragon
Recipe by Tout va bien! (tm) at https://christymajors.com/the-french-winophiles-rhone-gone-crazy/