Heat olive oil in a large skillet over medium-high heat. Cook and stir chicken and onion together in the hot oil until the chicken is completely browned and the onions tender, 7 to 10 minutes. Stir garlic, basil, kosher salt, and black pepper into the chicken mixture; cook for 1 minute.

Blend the tomatoes in a blender until smooth; pour over the chicken mixture and bring to a simmer. Cook mixture at a simmer until hot and the sauce has thickened slightly, about 10 minutes.

Sprinkle Parmesan cheese over the mixture; stir.