"Calce" means lime in Italian, but I am not sure if the "calce" in the name of these olives refers to their appearance or their flavor. With their vibrant, dark green color, the olives, which seem to be a specialty of Calabria, resemble little limes. Salty and rich from the oil in which they are packed, olives alla calce have the very subtle flavor of anise taken from the fennel with which they are cured.
(Come to think of it, perhaps there isn't any fruit involved in the production of these olives, and the name comes from the chemical.)
A babelfish translation of a description of how the olives are made:
Olives to the lime Of the variety ciucce. Greens are collected and they are put in wood troughs. For every 4 kg of alive olives 1,700 kg are taken of lime and 3 kg of oak ash and they are melted in the water in which the olives will be macerated. Made to rest for a day, they are removed from the water, they are washed with fresh water for 2-3 days. Then they are passed in troughs and in fresh water in which they are poured approximately 100 g of knows them, seeds of finocchio, leaves of bay and rametti of mirto.
Olives alla calce are $4.99/pound at Fairway.
Postscript (10/08/03): I contacted Fairway and traded a few emails back and forth with Steven Jenkins. He indicated that the olives are, in fact, cured with lime, or "lye," which serves to preserve their green color. There goes the lime (fruit) idea! Mr. Jenkins also described that the lye provides the mildest (blandest) cure. While these olives are, admittedly, blander than most others, I think that the mild cure allows you to taste the distinct fennel flavor. Steven Jenkins explains: "Why these people term them "alla calce" is to communicate to their public that the olives are lye-cured, therefore much milder, less olivey-tasting." Moreover, "The lye and aeration (oxygen) serve also to eliminate an olive's natural color. That Pugliese "alla calce" olive is a decidely unworldly hue."