Preheat your oven to 375°F (190°C). Place a rack in the middle of the oven.
Use a sharp knife to carefully slice each chicken breast horizontally, creating a pocket without cutting all the way through. You want a flap to open up for stuffing.
In a small bowl, combine chopped sun-dried tomatoes, fresh basil, and goat cheese to make a flavorful stuffing mixture.
Stuff each chicken breast generously with the mixture, pressing it in to fill the pocket completely. Secure the opening with toothpicks.
Heat olive oil in a skillet over medium-high heat until shimmering and fragrant. Carefully place the stuffed chicken breasts in the skillet.
Sear the chicken for about 3-4 minutes per side, until each side is golden brown and crispy. You should hear a satisfying sizzle.
Transfer the skillet or move the chicken to an oven-safe dish. Bake in the preheated oven for 20-25 minutes, or until the chicken is cooked through and juices run clear.
Remove the chicken from the oven and let it rest for 5 minutes. Carefully remove the toothpicks and slice the chicken to reveal the melty, colorful stuffing inside.
Serve the stuffed chicken breasts hot, with the filling slightly oozing out for a beautiful presentation and burst of flavor with each bite.