Boil chicken breast until cooked, then cut into small cubes. Place to the side.
Put tomato, cucumber, onion, pepper, garlic, and salt into a blender. Combine at high speed, slowly drizzling olive oil and balsamic vinegar into the blender as it blends.
Strain the puree through a fine mesh strainer into a large bowl.
Add the chicken cubes. Season to taste with salt and black pepper.
Top with chives, arugula leaves, and black olives.