Chicken Souvlaki with Tzatziki

Name: Chicken Souvlaki with Tzatziki
Ingredients: 2 pounds boned, skinned chicken breasts, cut into 1 1/2-in. cubes; 1/4 cup olive oil; 1/4 cup dry white wine; 2 tablespoons lemon juice; 2 teaspoons chopped fresh oregano leaves; 4 garlic cloves (2 crushed, 2 minced); 1 teaspoon kosher salt; 1/2 teaspoon pepper, divided; 1/2 English cucumber, coarsely shredded; 14 ounces nonfat Greek yogurt; 2 teaspoons distilled white vinegar