Preheat the oven to 400°F.
Heat 2 tablespoons olive oil in a large oven-safe skillet over medium-high heat until shimmering.
Add the 4 boneless, skinless chicken breasts to the hot oil and cook until lightly browned on the first side, about 3–4 minutes. Flip and brown the second side, about 3–4 minutes. It's okay if the chicken is not fully cooked at this point. Remove the chicken from the skillet and set aside on a plate.
Add the 1 medium yellow onion (sliced into thin strips), 3/4 cup sun-dried tomatoes (roughly chopped; do not use oil-packed tomatoes), and 2 minced garlic cloves to the same skillet. Cook, stirring often, until the onion is soft and translucent, about 4–5 minutes.
Stir in 1 teaspoon Italian seasoning, 1 1/2 cups light coconut milk, and 1 cup chicken broth. Bring the mixture to a gentle simmer.
Return the chicken breasts to the skillet, nestling them into the sauce and spooning some sauce over the tops.
Cover the skillet tightly with foil and transfer it to the preheated oven. Bake for 15–20 minutes, or until the chicken is cooked through (internal temperature 165°F / 74°C).
Remove the skillet from the oven, uncover, and sprinkle the chicken with 1/4 cup fresh basil (roughly chopped). Let rest for 3–5 minutes, then serve hot.