Put arugula and romaine in a large serving bowl. Top greens with chicken, fennel, and pistachios.
Cut the peel and outer white membrane from 2 grapefruit. Slice grapefruit into half moons and add to salad.
Juice remaining grapefruit into a bowl. Add oil, sugar, salt, and pepper to juice and whisk together. Pour over salad and toss gently to mix.
Note: Nutritional analysis is per serving.