In a medium saucepan, add chicken, salt, enough water to cover, about 2 cups. Bring to a boil, reduce heat to low, and simmer 15-20 minutes, or until internal temperature reaches 165℉. Take chicken out of water and set aside to cool.
Once cool enough to handle, shred chicken using 2 forks.
In a small bowl, whisk together remaining 2 tablespoons olive oil, mustard, lemon juice. Season with salt and pepper to taste.
To serve, place wraps on work surface. Spread ¼ cup lettuce across the center of each wrap. Top with avocado, egg, blue cheese, bacon, chicken, and tomato. Drizzle dressing over top. Roll up and serve.