Rinse, and pat dry chicken thigh. Season each chicken thigh with salt and pepper to taste.
In a large heavy skillet, like cast iron, over medium-high heat, add olive oil and butter. Melt butter. Carefully add seasoned chicken thighs skin down, and cook for 10-15 minutes until edges of skin become golden brown. You may want to use a splatter screen to prevent oil from popping on you during cooking. Using tongs carefully turn each chicken thigh over.
Brown bottom of each chicken thigh until juices run clear, or internal temperature reaches 165° on a meat thermometer. Using tongs remove chicken and place on plate. Set aside while making the Mushroom wine sauce. Do NOT drain skillet of pan juices.
Turn heat down to medium. Add mushroom, garlic, and onion to pan juices. Saute for 5 minutes until mushrooms are soft, and onions are translucent.
Add chicken broth and wine. Stir. Simmer for five minutes. Add heavy cream, stirring to combine. Reduce heat to a low simmer. Add 2 sprigs of rosemary, chives, and 3-4 sprigs of fresh thyme. Stir to incorporate allowing herbs to release their flavor in the sauce. Simmer an additional 3-4 minutes.
Add cooked chicken thighs back into the skillet with the mushroom wine sauce and continue to simmer 5-10 minutes until cream sauce reduces by half, about 5-10 minutes.
Remove skillet from heat. Spoon sauce over chicken. Garnish with the remainder of rosemary, thyme, and parsley. Serve over steamed rice or noodles.