In a blender combine mayonnaise, lemon juice, olive oil, mustard, Worcestershire sauce, Parmesan cheese, garlic, and anchovy.
Season with salt and pepper to taste. Process until smooth.
Cover and refrigerate until needed.
Season the chicken breasts on both sides with salt and pepper.
Lightly grease the grates of an outdoor grill. Heat the grill to medium-high heat.
Add the chicken breasts onto the grill and cook for 6-8 minutes per side or until the chicken is fully cooked (the internal temperature has reached 165 degrees F.).
Remove the chicken from the grill and chop it into small chunks.
Cook the rotini pasta according to package directions. Drain and rinse with cold water.
In a large bowl toss the pasta and chicken with the romaine lettuce. Pour the dressing over the salad. Add the parmesan cheese and toss to combine and coat. Season with salt and pepper.