In a colander, thoroughly rinse the chickpeas in water. Pat dry with paper towels and spread out on a baking sheet to air-dry for 1 hour.
Pour the vegetable oil into a deep, heavy pot to a depth of about 2 inches. Heat the oil to 375°, add one-third of the chickpeas and fry for 2 minutes, until brown and crisp. Drain on paper towels. Fry the remaining chickpeas in two more batches. While still warm, toss the chickpeas with the sea salt and pimentón and serve.