Cook the pasta according to the package instructions in a large pan of lightly salted boiling water. Once it achieves an al dente consistency, drain the pasta well.
Meanwhile, heat 1 tablespoon olive oil in a large frying pan over high heat. Add the tuna and cook, stirring occasionally, for 2 to 3 minutes until seared. Remove the fillets from the pan and set them aside.
Return the pan to high heat, and add the remaining oil, garlic, chiles and anchovies. Cook, stirring, for 1 minute.
Add in the tomatoes and olives, and cook, stirring occasionally, for an additional 5 minutes or until the tomatoes are slightly softened.
Incorporate the hot pasta and tuna to the pan, and gently toss the ingredients. Drop in the basil leaves and season the dish with salt and pepper, to taste. Serve immediately.