1. Pat chicken dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in large skillet over medium-high heat until just smoking. Cook chicken until golden, about 3 minutes per side. Transfer to plate.
2. Heat remaining oil in empty skillet over medium-high heat until shimmering. Cook onion until softened, about 5 minutes. Add garlic, oregano, and pepper flakes and cook until fragrant, about 30 seconds. Stir in tomatoes, cream, and 1/4 teaspoon salt and bring to boil. Return chicken and any accumulated juices to skillet. Simmer, covered, until chicken is cooked through, about 10 minutes.
3. Transfer chicken to platter and tent with foil. Simmer sauce, uncovered, until slightly thickened, about 5 minutes. Off heat, stir in basil and season with salt and pepper. Pour sauce over chicken. Serve over pasta.