Trim any excess fat from the chicken breasts and slice in half lengthwise to make two thin cutlets. Season both sides of the chicken breasts evenly with 1 teaspoon of kosher salt and the freshly ground black pepper then dredge each breast in the flour, shaking off any excess.
Heat 2 tablespoons butter with the canola oil in a large skillet (do not use non-stick) over medium-high heat. Add the chicken and cook for 2-3 minutes per side. Transfer to a platter or sheet pan and cover with foil.
Return the skillet to medium heat. Add the shallot and cook, stirring for 1 minute. Add the wine and cook for 1 minute, while scraping the pan. Then add the chicken stock and bring to a boil until the liquid reduces by half, about 2 minutes. Whisk in the cream and cook for 1 minute. Remove from heat and which in the remaining tablespoon of butter and the Dijon mustard. Stir in the remaining ½ teaspoon of salt and add the chicken breasts back to the skillet, spooning the sauce overtop. Top with chives before serving.
