Bring a large pot of salted water to a boil and cook the spaghetti according to package directions until al dente.
Drain the pasta, reserving 1/2 cup of the cooking water, and set the pasta aside.
While the pasta cooks, cook the grilled pesto chicken and cherry tomatoes according to the referenced recipe; keep the chicken warm and halve or slice tomatoes if needed.
Return the drained spaghetti to the pot or a large skillet over low heat. Add 1 cup pesto and 1/2 cup reserved pasta water and toss until the pasta is evenly coated and the sauce is smooth, adding more reserved water a tablespoon at a time if needed.
Divide the pesto-coated spaghetti among serving bowls, top with sliced grilled chicken and the cooked cherry tomatoes, and finish with a pinch of freshly grated parmesan.
Notes
Use homemade basil pesto for best flavor, or store-bought when short on time.
Reserve pasta water to loosen the sauce as needed.
Slice the chicken just before serving to retain juiciness.