Chicken Souvlaki with Tzatziki

Ingredients

• pounds boned, skinned chicken breasts, cut into 1 1/2-in. cubes
• olive oil
• dry white wine
• tablespoons lemon juice
• teaspoons chopped fresh oregano leaves
• garlic cloves
• teaspoon kosher salt
• teaspoon pepper, divided
• English cucumber, coarsely shredded
• ounces nonfat Greek yogurt
• teaspoons distilled white vinegar