For those seeking the ultimate getaway, it is possible to rent the tiny Greek island of Argironisos. Offering complete privacy in an atmosphere of luxury and comfort, this secluded island, known as ''Silver Island,'' is between the island of Evia and the Greek mainland in a channel of the Aegean Sea.
The picturesque 60-acre island is covered with wildflowers and oak, cypress, and olive trees, with a lighthouse standing on the eastern point. Argironisos is dotted with secluded, sandy coves for sunbathing and lined with winding paths for walking.
From two to six guests can be accommodated in the island's whitewashed, century-old traditional Greek home, decorated with native handicrafts and ancient Greek artifacts. The villa has three double bedrooms, a fourth bedroom with bunks, two modern baths, and a fully equipped kitchen.
All meals on the island, using ingredients from local farms, are provided. A small fleet of boats, including a 30-foot motor-sailing sloop, is provided for guests.
Daily fees for rental of the island include all personal services such as laundry, house cleaning, and baggage handling, all meals, water craft, and aquatic sports. The fee for a party of six is $1,200 per day; for four, $900 per day; and for two, $500 per day.
Further information may be obtained from the Greek National Tourist Organization at 645 Fifth Avenue, New York, N.Y. 10022; 611 West Sixth Steet, Los Angeles, Calif. 90017; or 168 North Michigan Avenue, Chicago, Ill. 60601.