In a food processor, combine the peeled cucumbers, fresh dill or chives, chopped garlic, olive oil, chopped onion, white wine vinegar, sugar, salt, and black pepper.
Process until smooth.
While the processor is running, gradually add the water until the mixture reaches a smooth consistency.
Cover the gazpacho and refrigerate it for at least 2 hours, or overnight, to chill and allow the flavors to meld.
Before serving, taste the gazpacho and adjust the seasoning with more vinegar or salt if necessary.
Pour the chilled gazpacho into individual bowls and serve cold.