Put a large pot of salted water on to boil for the pasta.
Drain the chicken livers and using kitchen shears, cut them into small pieces (about 1/2-inch). Set aside.
Heat the olive oil in a pan over medium heat and add the onion. Sauté until the onion is soft and translucent, 3 to 4 minutes, then add the garlic and cook until fragrant, 1 minute longer.
Add the chicken livers and cook, stirring often, until nicely browned, 4 to 6 minutes. Add the tomatoes, balsamic vinegar and thyme. Season to taste with salt and pepper and simmer gently for 6 to 8 minutes, stirring occasionally.
While the ragu simmers, cook and drain the pasta according to package directions. Return the pasta to the pan, add the ragu and toss to combine.
Note: If the pasta seems dry, add an extra drizzle of olive oil.