Bring a large pot of salted water to boiling. Add the pasta and cook until just tender according to the package instructions.
Meanwhile, in a food processor, combine the parsley, chives, walnuts, and garlic and pulse a few times to create a coarse paste. With the machine running, pour the olive oil through the feed tube until the mixture becomes a smooth puree. Add half of the Parmesan and puree until just combined. Season with pepper.
Drain pasta and place in a large bowl. Toss with the pesto. Sprinkle with the remaining cheese to serve.