Sprinkle chicken with ¼ teaspoon each salt and pepper. Heat oil in a large skillet over medium-high heat. Add the chicken and cook, turning once, until cooked through, 6 to 8 minutes total. Transfer to a plate.
Reduce heat to medium. Add mushrooms and cook, stirring, for 1 minute. Add spinach, cover and cook, stirring once, until the mushrooms are tender, 2 more minutes. Whisk heavy cream, sour cream, vinegar, garlic powder, onion powder and the remaining ¼ teaspoon each of salt and pepper together in a measuring cup. Add to the pan along with any accumulated juices from the chicken; simmer, stirring, until slightly thickened, 1 to 2 minutes. Return the chicken to the pan and turn to coat. Serve the chicken topped with the sauce.
