Bring a large pot of salted water to a boil. Add spaghetti or linguine and cook until al dente, about 8-10 minutes. Reserve 1/2 cup of cooking water before draining.

Heat olive oil in a skillet over medium heat. Season chicken with salt and pepper, then sear for 5-6 minutes on each side until golden brown and cooked through. Transfer to a plate to keep warm.

In a food processor, combine basil, pine nuts, garlic, and Parmesan. Pulse while drizzling in olive oil to create a smooth pesto. Add reserved pasta cooking water if needed.

Return chicken to the skillet, add drained pasta and pesto, tossing to coat. Stir in lemon zest and additional pasta water for desired texture.

Taste and adjust seasoning if necessary. Serve immediately, garnishing with extra Parmesan and olive oil.