Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente; drain and set aside.
While the pasta cooks, heat the olive oil in a large skillet over medium-high heat.
Season the thinly sliced chicken breasts with salt and pepper, then add them to the hot skillet. Cook about 2–3 minutes per side until roughly 80–90% cooked through (timing varies with thickness).
Pour the can of petite diced tomatoes with their juice into the skillet, aiming to distribute the liquid around and between the chicken pieces rather than directly on top.
Sprinkle the dried oregano, 1/2 teaspoon pepper, and optional 1/2 teaspoon salt over the skillet. Bring to a boil and cook 3–5 minutes, until some tomato liquid has evaporated.
Reduce heat to low, evenly top each chicken piece with the mozzarella, cover the skillet, and cook 1–2 minutes until the cheese melts.
Stir in the torn or chopped basil and cook about 1 minute until the basil wilts slightly and is incorporated into the tomato sauce.
Serve the chicken and tomato mixture over the cooked pasta while warm.