Cook the pasta in a large pot of boiling salted water until tender but still firm to the bite, stirring occasionally, about 8 minutes.
Whisk the oil, parmesan, and lemon juice in a large bowl to blend.
Prepare the chicken breasts for the grill. Optional but encouraged: use a meat tenderizer to pound out the chicken to make it thinner (this will also speed cooking time! If you do not do this you may need an additional few minutes for grilling time.) Season with a sprinkling of salt and pepper.
To grill: preheat your grill to medium high and lightly oil the grates. Place chicken on the grill for 5-6 minutes until grill marks appear.
Flip and cook for another 5-6 minutes or until done.
Once the pasta is cooked, drain the pasta, reserving 1/4 cup of the cooking liquid. Toss the pasta with the lemon sauce, and the reserved cooking liquid, adding 1 tbsp at a time as needed to moisten. Season with salt and pepper.
Slice the grilled chicken and place on top of spaghetti. Garnish with lemon zest and chopped basil. Enjoy!