Step 1Heat the oven to 400 degrees and line a jellyroll pan with parchment paper.
Step 2Two at a time, place the chicken breasts, smooth side up, between 2 sheets of plastic wrap. Using a meat mallet, gently and evenly pound the chicken to about 1/4-inch thick.
Step 3Place each pounded chicken breast lengthwise on the parchment-covered pan, smooth side down. Season with salt and pepper. Spread the pesto over the surface of the chicken, dividing evenly. Press 3 spinach leaves on top of each breast and add 2 teaspoons of goat cheese. Very gently and tightly, roll the chicken away from you. Rub the top of each roulade with olive oil and season with salt and pepper.
Step 4Roast the roulades until the internal temperature reaches 165 degrees, about 20 minutes. At the 18-minute mark, cut one of the roulades in half to check if the chicken is cooked through; if not, return to the oven for 2 to 3 minutes.