Bring a large pot of well-salted water to a boil and cook the pasta until al dente according to package instructions. Reserve ½ cup pasta water, then drain.
Season the chicken pieces evenly with salt and black pepper.
Heat olive oil in a large skillet over medium heat and cook the chicken for 6–8 minutes until golden and fully cooked. Remove from the pan and set aside.
Reduce heat to low and add minced garlic to the same skillet. Cook for 30 seconds until fragrant.
Stir in the pesto and add heavy cream or butter if using, keeping the heat low to preserve flavor.
Return the cooked chicken and pasta to the skillet.
Add reserved pasta water a little at a time and toss until the sauce coats everything evenly.
Remove from heat and stir in Parmesan cheese.
Finish with lemon zest, fresh basil, and optional tomatoes or olives.
Serve immediately while warm.