Season the chicken breasts with salt and pepper.
Dredge them lightly in flour, shaking off any excess.
Heat oil and butter in a large skillet over medium heat.
Add the chicken and cook until golden brown, about 5 minutes per side.
Remove chicken from the skillet and set aside.
Add white wine to the skillet and bring to a boil, scraping any brown bits from the pan.
Pour in the chicken broth and let it reduce slightly.
Stir in the cream and continue to cook until the sauce has thickened, about 3 minutes.
Return the chicken to the skillet, turning it to coat in the sauce.
Add fresh spinach and let it wilt, cooking for an additional 2 minutes.