Cut the chicken into 1-inch pieces and sprinkle lightly with salt and pepper.
Heat a large skillet over medium heat. Once hot, add the oil and swirl to coat. Add the chicken and sauté until nicely browned and cooked through, 7 to 10 minutes. Transfer chicken to a bowl.
Add the butter to the pan and let melt. Once melted, add the prosciutto and sage. Cook until the butter is a deep amber (careful not to burn it), about 4 minutes. Remove from heat and add the chicken back into the pan. Toss to coat in the sauce.