Make the chicken breast halves thin by placing them between two layers of parchment paper or plastic wrap and pounding them with a meat mallet until they are about ½ inch thick.
In a large skillet over medium heat, heat the oil and butter until melted. Cook the chicken breast halves for 3 minutes on each side or until brown and cooked through. Transfer to a dish and keep warm.
Using the same skillet, cook the spinach with the salsa until the spinach has wilted and the mixture is heated through.
Serve the chicken breasts with the spinach sauce on top.