Mix the marinade and tzatziki sauce. In a mixing bowl, add the minced garlic, lemon juice, 1 tablespoon of extra virgin olive oil, plain Greek yogurt, dill, thyme, salt, and pepper. Mix until combined. Divide into 2 bowls. Add the chicken to one of the bowls, using tongs to turn to coat well. Let marinate for about 30 minutes. Add the shredded cucumber to the other bowl and stir well.
3 tablespoon olive oil, 4 cloves garlic, 1/3 cup lemon juice, 3/4 cup plain Greek yogurt, 1 teaspoon fresh or dried dill, 1 teaspoon dried thyme, 1 teaspoon salt, 1/2 teaspoon pepper, 1 pound chicken breasts, 1 small cucumber