Whisk the extra virgin olive oil with the balsamic vinegar, sugar, tarragon, salt and freshly ground black pepper in a bowl for approximately. 5 minutes.
Place the chicken breasts in a shallow dish and cover with half of the dressing. Refrigerate for at least 1 hour.
Remove the breast from the fridge at least 30 minutes before cooking.
Heat 1 teaspoon of the olive oil in a pan. Place the chicken breasts in the hot pan and seal on both sides until brown. Reduce the cooking temperature to medium low and cook the chicken for 15 to 20 minutes, turning every 5 minutes until the chicken is cooked through.
Remove from the heat and let the chicken rest for 5 minutes. Slice the chicken into thin pieces.
Arrange all the ingredients in a bowl, drizzle the salad dressing over and top with the toasted almonds.