Measure out the yogurt into a metal strainer or coffee filter in a medium bowl. Place in the refrigerator and allow liquid to strain from the yogurt for several hours. Set aside.
Peel and grate the cucumber. Drain the liquid from the cucumber in a metal strainer. It may help to use the back of a spoon to help squeeze out any excess liquid.
In a medium bowl, combine shredded cucumber, garlic, yogurt, salt, pepper, lemon juice, dill, chives and refrigerate for a few hours before serving.