Bring a large pot of salted water to a boil, add spaghetti and cook according to package directions, stirring often, until al dente. Reserve 1 1/2 cups cooking liquid from pasta. Drain spaghetti in a colander and reserve.
Heat oil over medium heat in same pot. Add onion and cook, stirring, until softened, about 5 minutes. Return pasta to pot along with tomato, chicken and pasta liquid. Toss well and season with salt and pepper to taste.
Transfer pasta to plates. Sprinkle with basil, dot with crumbled goat cheese and serve immediately.