Put the chicken breasts between sheets of plastic wrap and pound until they are 1/4 inch thick. Sprinkle with salt, pepper, and garlic powder then dredge in flour.
Heat 2 teaspoons of olive oil in a large skillet over medium high heat. Add the chicken and cook 3-4 minutes per side, or until golden brown. Remove chicken from the pan and put on a plate. Keep warm.
Heat the remaining olive oil in the same skillet. Add the shallots and garlic cooking for 1-2 minutes, scraping the bottom to get the brown bits. Sprinkle with 1 tablespoon of flour and stir to coat.
Add the wine and broth to the skillet and bring to a boil. Return the chicken to the pan and reduce to a simmer.
Cook until the chicken is heated through, about 3-4 minutes. Stir in the sour cream, mustard, lemon juice, and chopped chives. Flip the chicken to coat in the sauce.
Serve the chicken with a spoonful of the sauce and fresh chives sprinkled on top.