Trim chicken and place between sheets of plastic wrap; pound with a meat mallet or heavy skillet until flattened to an even thickness, about 1/2-inch.
Season both sides of chicken with 1/2 teaspoon of salt. Place 1/3 cup of the flour on a plate and dredge chicken; discard excess flour.
Heat 1 tablespoon of oil in a large skillet over medium-high heat; add chicken and cook until golden brown, 1 to 2 minutes per side; transfer to a plate, cover with foil wrap and keep warm.
Heat remaining oil in the skillet; add onion and cook for 1 to 2 minutes or until translucent, stirring constantly and scraping up all of the browned bits from the bottom of the pan.
Sprinkle with remaining flour and stir to coat onion. Add wine (or juice/vinegar), broth and remaining salt; bring to a boil, stirring often.
Return chicken to the pan along with any accumulated juices. Reduce heat and simmer until chicken is heated through and no longer pink in the center, about 6 minutes. Stir in sour cream and mustard until smooth; turn chicken to coat with the sauce.
Stir in chives and serve immediately.