Preheat oven to 400°F (200°C) and set a large pot of salted water to boil for pasta.
Pat chicken dry and season with 1/2 tsp salt and 1/4 tsp black pepper.
Heat 2 tbsp olive oil in an oven-safe skillet over medium-high heat. Sear chicken 2-3 minutes per side until golden. Transfer to oven and bake 10-12 minutes until fully cooked (165°F internal temp). Remove and let rest.
In the same skillet, add 1 tbsp olive oil, then sauté garlic 1 minute until fragrant. Add cherry tomatoes and cook 4-5 minutes until softened and slightly burst. Stir in oregano, red pepper flakes (if using), and 1/4 tsp salt.
Cook spaghetti in boiling water 8-10 minutes until al dente. Reserve 1/2 cup starchy pasta water, then drain.
Add pasta to the skillet with tomato mixture, tossing to coat. If sauce is too dry, add 1-2 tbsp reserved pasta water to loosen. Stir in lemon juice and 1/4 cup Parmesan.
Thinly slice chicken and serve pasta on plates with a chicken portion on top. Garnish with remaining basil and Parmesan.