Season the chicken with salt; place the broth (or water) and chicken in a small stockpot. Bring to a simmer over medium heat, cover, and cook until chicken is just done, about 10 minutes. Remove breasts; cool, shred, and set aside. Reserve broth for future use.
Place basil, vinegar, garlic, oil, and salt to taste in blender. Blend until smooth and set aside.
In a large bowl, toss arugula, radicchio, lettuce, fennel, red pepper, onion, walnuts, 1/2 cup salad dressing, and salt and pepper to taste. Place three endive leaves in a three-pointed star with tips facing out on four individual dinner plates or wide shallow bowls. Place equal mounds of salad in center. Arrange chicken on top.
AFTER READING THE INGREDIENTS, SHOWED MY HUBBY WHO SAID "WOW! THAT LOOKS GOOD" AND OFF TO STORE HE WENT. GUESS WHAT WE ARE HAVING FOR DINNER? THANKS MARTHA