Cut chicken into 2" chunks. Heat water to boiling. Add salt. Stir chicken into boiling water, immediately reduce to just below a simmer and cook 10 minutes. Remove from heat and let chicken stand in cooking water 5 minutes. Drain and rinse chicken under cold water to stop the cooking process. Pat dry.
By hand, shred chicken into bite-size pieces and place in mixing bowl. Add the pecans, celery, onion, carrot, blue cheese dressing, and vinegar. Mix until well combined.
To serve, mound a scant 1/2 cup chicken salad in center of each serving plate and spread slightly to flatten to a round the same width as tomato. Top with a slice of red tomato. Mound another scant 1/2 cup salad mixture on top and arrange a yellow tomato slice on top. Garnish, if desired, with parsley sprig and pecan; serve.