With a peeler, slice cucumber into 8 1/8-inch thick slices lengthwise. Cut each slice into 3 pieces crosswise.
Place about 1 teaspoon shredded carrot onto the bottom edge of a cucumber slice; place about 1 teaspoon cream cheese onto the carrot, and press 2 or 3 raisins into the cream cheese. Roll the cucumber slice into a little sushi roll, starting at the filled end. Tie roll with a chive to secure. Repeat with remaining ingredients.
