In a bowl big enough to hold everything, whisk together the jalapeno, garlic, lime juice, and salt and pepper.
Whisk the oil into the mixture in a thin stream, until blended and emulsified.
Stir in the cucumbers, being sure to get them well coated.
Make at least 1 hour ahead of time to blend the flavors – it is best eaten the day you make it, but if needed, leftovers should be stored in the fridge