Preheat the oven to 400° and line a baking sheet with a wire rack. On a cutting board, lay out the chicken breasts, skin-sides down, and cover with a layer of plastic wrap. Using a mallet, pound the breasts until they are 1/2 inch thick.
In a small bowl, mix together the rosemary, sage, thyme, lemon zest and garlic, then rub onto the chicken. Season with salt and pepper. Lay 1 slice of prosciutto over each breast and roll lengthwise. Using butcher's twine, secure each roll with a series of 3 knots. Season the rolls with salt and pepper. Wrap each roll tightly with plastic wrap and refrigerate for 1 hour.
In a 12-inch skillet, heat the olive oil over medium-high heat. Remove the chicken rolls from the plastic and cook, turning as needed, until golden brown, 6 to 8 minutes. Transfer each to the prepared baking sheet. Roast in the oven until they've reached an internal temperature of 165°, 8 to 10 minutes more. Let rest 5 minutes before removing the butcher's twine, slicing and serving.