Heat olive or coconut oil in large skillet over medium-high heat until whisps of smoke appear. Gently place each chicken breast in the skillet, careful not to overcrowd it. Season the other side of each chicken breast while it cooks. Allow the chicken to sear for about 4 minutes per side. Set aside to rest for at least 10 minutes.
Lower heat to medium-low. Remove pan from heat, you should have lots of delicious brown bits stuck to the bottom of the pan. Deglaze those yummy bits with the white wine, stirring with a wooden spoon. Bring skillet back to the heat and allow the white wine to reduce just slightly, about 2-3 minutes. Turn off the heat, stir in the butter and fresh herbs. Pour over the chicken and serve.