There are places more remote, but Tristan Da Cunha is inhabited, even though the 270 residents only see a mail ship once a year!
When Napoleon was sent to St. Helena by the British, they annexed the closest chain of islands to prevent the French from attempting to rescue him. After all, who wouldn't travel a mere 2430 km over rough and hostile seas in order to rescue the Emperor himself? Yes, that's right, the islands of Tristan Da Cunha closest neighboring land mass, the island of St. Helena, is 2430 km away.
Tristan Da Cunha has a radio station, a convenience store, beautiful wildlife, and an active volcano! Link