Cook the pasta in a large pot of boiling salted water, until al dente. Drain well.
Season chicken with salt and pepper. Heat a large grill pan over medium high and add chicken. Grill until golden and completely cooked. Remove to a plate and slice.
Add the garlic and red pepper flakes to a saute pan with 3 tablespoons of olive oil and saute until fragrant. Add the cooked pasta and turn heat off. Mix all together.
Remove pasta to a large bowl. Add chicken to the warm pasta and season with salt and pepper. Sprinkle in chopped parsley. Add the juice of 2 lemons and mix. Before serving top with Parmesan.