Chop chicken thighs into bite-sized pieces. Season chicken with salt and pepper. Heat a skillet with olive oil. Cook chicken for about 4 minutes on medium heat. Stir and then cook for another 4 minutes until cooked through. Set aside.
Boil a large pot of salted water. Add pasta and cook al dente, according to the package.
In a small bowl, whisk oil, cheese, and lemon juice until blended.
Drain the pasta, reserving 1/4 cup of pasta water. Toss the pasta with the lemon sauce and reserved pasta water, adding 1/4 cup at a time. Season with salt and pepper. Add chicken and stir. Garnish with more cheese and chopped basil.