Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Drain, reserving 1/2 cup pasta water.
While pasta cooks, season chicken strips with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until golden and cooked through, about 4-5 minutes per side. Remove chicken from skillet and set aside.
Reduce heat to medium. Add minced garlic to the skillet and sauté for 30 seconds until fragrant. Pour in heavy cream, pesto, and Parmesan cheese. Stir until smooth and simmer for 1-2 minutes.
Return chicken to the skillet. Add drained pasta and toss to coat. If sauce is too thick, add reserved pasta water a tablespoon at a time until desired consistency. Adjust seasoning with salt and pepper.
Serve immediately, garnished with fresh basil if desired.
Tips
For extra flavor, use sun-dried tomato pesto instead of basil pesto.
Substitute chicken with shrimp or tofu for variation.
Store leftovers in an airtight container in the refrigerator for up to 3 days. Reheat gently with a splash of milk or cream.