Slice the cucumber into rounds about the thickness of a nickel. Combine in a nonreactive bowl with the vinegar, sugar, and 1 teaspoon of the salt. Allow to sit for 20 to 30 minutes at room temperature.
Drain off the cucumber liquid. Mix the cucumbers with the sour cream, dill, remaining 2 teaspoons salt, and the pepper. Cover and refrigerate for 1 hour.