In a small saucepan with a tight-fitting lid, cover the chicken breast with 2 inches of water. Bring the water to a boil, reduce to a simmer and cook for 15 minutes. Remove the chicken breast and let cool.
Meanwhile, pulse the almonds in a food processor until finely chopped. Add the tomatoes, cucumber, red onion, garlic, vinegar, lemon juice, olive oil and the handful of cilantro and pulse until coarsely chopped. Season the gazpacho to taste with salt and pepper and chill in a covered container in the freezer for 20 minutes, stirring every 5 minutes.
Shred the poached chicken. Remove the soup from the freezer and adjust the seasoning if necessary. Divide the gazpacho among 4 bowls, top with the shredded chicken and garnish with cilantro.