Stuff each olive with feta, completely filling it up. Wipe the olives clean with kitchen towel. Mix the flour, pepper and chilli in a shallow dish. Put the egg in another dish and the breadcrumbs into a third. Roll the olives in flour, then in egg and finally in breadcrumbs, to coat all over. Set aside.
Heat the oil in a pan until almost smoking. Put in a third of the olives, enough to fit without overcrowding; don't drop them or you risk a splatter. Fry for 20 seconds, until golden brown, remove and drain on paper towel. Repeat with the other olives. Serve warm, or at room temperature.