Grate the cucumber. Squeeze out all the extra liquid using a cheesecloth or a fine-mesh strainer. Set the cucumber aside.
Grab a medium bowl. Combine the Greek yogurt, minced garlic, chopped dill, olive oil, lemon juice, salt, and black pepper. Mix it all together well.
Add your drained cucumber to the yogurt mixture. Stir gently until everything is combined.
Cover the bowl with plastic wrap. Pop it in the refrigerator for at least one hour so the flavors can mingle.
Serve your chilled dip with your favorite veggies, warm pita bread, or crunchy crackers.