Heat oil and 1 Tablespoon of the butter in a large skillet over medium heat.
Add chicken and saute until browned on bottom (about 5 min), flip and saute on remaining side until cooked through (about 5 more min).
Remove from pan, transfer to an oven-safe platter, cover, and keep warm in preheated oven.
Add remaining 1 Tablespoon butter to skillet and melt over low heat.
Add shallots and cook until softened (3-5 min).
Pour in wine and bring to a boil, stirring often, until wine is reduced to around 1/4 cup.
Add broth and boil until mixture is again reduced to around 1/4 cup.
Add cream, salt & pepper and simmer over medium heat until thickened (about 5-7 min).
Stir chives into sauce and serve drizzled over warm chicken.
Nutrition Info Per Serving: Calories 531 Total Fat 30 g Cholesterol 229 mg Sodium 282 mg Potassium 877 mg Total Carbohydrate 3 g Dietary Fiber 0 g Sugars 2 g Protein 54 g