Sprinkle chicken with 1/4 teaspoon each salt and pepper. Heat oil in a large skillet over medium heat. Add the chicken and cook, turning once, until browned and cooked through, about 6 minutes. Transfer to a plate.

Add garlic to the pan and cook, stirring, for 30 seconds. Increase heat to medium-high and add wine. Cook until slightly reduced, about 1 minute. Return heat to medium and stir in spinach, cream and the remaining 1/4 teaspoon each salt and pepper. Simmer for 2 minutes. Return the chicken to the pan and turn to coat with the sauce.