Strain the yogurt using a metal strainer or a coffee filter for a few hours to remove as much liquid as possible. Set aside.
Scoop seeds out of the cucumber with a small spoon. Place cucumber in a mini food processor or grate with a box cheese grater. Drain the liquid from the cucumber in a metal strainer and sprinkle with a little salt (this helps release the liquid). You may want to use the back of a spoon to help squeeze out any excess liquid.
Combine strained cucumber, garlic, yogurt, salt, pepper, lemon juice, dill, chives and refrigerate at least 1 hour before serving.
Makes about 2 cups. Store in refrigerator for about a week.