Heat a large, heavy skillet on high heat.
Toss raw diced chicken in 4 tbsp of prepared chimichurri sauce as a marinade as grill comes to temperature. (Don't toss chicken in the sauce, remove a bit to add to the raw chicken to prevent cross contamination.)
When pan is hot, toss chicken in pan and sauté, stirring occasionally, until browned and cooked through to an internal temperature fo 165 degrees- about 6 minutes.
Add water to a large stock pot and bring to boil.
Generously salt water and add in pasta.
Cook pasta to just under al dente (should be flexible but with a bit of crunch still.)
Remove 1 cup of pasta water and add to pan with chicken, bring to a boil.
Drain pasta and add to pan with chicken and boiling pasta water.
Stir in 1/2 cup chimichurri sauce and toss as pasta water cooks down.
Taste and add up to 1/2 cup more chimichurri sauce, depending on your taste.
Garnish with parmesan cheese and serve.