Combine first 6 ingredients and mix well. Place chicken in a ziplock bag and pour marinade over chicken. Marinate a few hours to overnight in the refrigerator.
When ready, grill until done. Allow chicken to rest for a few minutes and then slice into strips to serve over pasta.
While chicken is grilling. Cook pasta according to directions (10-12 minutes). Reserve 1/2 cup of pasta water and drain.
In the same saucepan, melt butter over medium heat. Whisk in garlic and lemon juice. Pour in half-and-half and whisk until hot. Add some salt and pepper to taste. Add the parmesan cheese, basil and capers, and heat until cheese is melted.
Check the consistency of the sauce and add some of the reserved pasta water to loosen the sauce if necessary. Toss in pasta.
Serve in pasta bowls with grilled chicken on top. Sprinkle with more parmesan if desired.