Whisk the yogurt, garlic, lemon juice, lemon zest, and 3/4 teaspoon of the salt together in a medium bowl.

Place the chicken in a 6-quart slow cooker. Sprinkle evenly with 3/4 teaspoon of the salt. Pour over ⅓ cup Greek yogurt sauce over the chicken, tossing to coat. Cover the remaining yogurt marinade and refrigerate while the chicken cooks.

Cover the chicken and cook on high for 2-4 hours or on low for 4-6 until the chicken is tender and cooked through.

Once cooked, remove the chicken from the cooking liquid. Slice into strips or shred with two forks. Strain the cooking liquid, and add ¼ cup cooking liquid back to the slow cooker.

Add the chicken back to the slow cooker, then pour over ⅓ cup of the reserved Greek sauce marinade, tossing to coat. Gently warm through on high for 5 minutes.

Serve with the remaining ⅓ cup Greek sauce marinade on the side for dipping or drizzled on top.