Trim the ends from the cucumbers and scrub the peels.
Remove about half of the peels from each cucumber and remove the seeds if they are large.
Cut the cucumber into chunks and put in a food processor or blender.
Pour in the orange juice and sprinkle in the sugar and oregano. Blend for at least 1 minute or until very finely puréed. The drink should be a bit thick and slightly foamy. Taste for sweetness and seasoning and adjust as needed.
Pour into a pitcher, cover, and refrigerate until chilled.
Serve in tall glasses or in small bowls with spoons.
