During the reign of John Paul II, seminarians studying in Rome had a custom of sending a chalice they were planning to use once they were ordained to the priesthood to the pope, who would use the chalice at one of his private Masses and then have it returned to the seminarian. In fact there was a lovely story soon after the election of Pope Benedict XVI of one seminarian who had asked then-Cardinal Joseph Ratzinger to consecrate his chalice, thinking he would then send it to John Paul for its first use. But Cardinal Ratzinger was impressed with the beauty of the chalice and asked to use it at a Mass he was about to celebrate. The seminarian agreed, then sent the chalice to John Paul afterward. And that is how that seminarian ended up having his chalice used by two popes. Whether or not the custom continues during Benedict XVI’s reign, I do not know.
In any case, this has been a custom for those who have a legitimate need to own a chalice because of their own priestly ministry. Chalices, once consecrated and used during Mass, are sacred liturgical vessels, and are not intended to be objects of private devotion for laypeople. Even if Pope Benedict has continued the custom of his predecessor for seminarians studying in Rome, it is not appropriate for laypeople to buy a chalice with the intent to have it made over into a “relic” for their personal use. Instead, if you happen to be in Rome, and if you happen to have the privilege to attend a papal audience, you can take along a rosary or other such sacramental, and have it blessed during the papal audience.