The chalice, being a consecrated vessel, has been kept covered out of reverence for it. Now, the immediate preparation for the Sacrifice begins with the removal of the veil because Divine mysteries of our Faith are about to be revealed.
We may recall that Our Lord was unvested, and pray thus: “O Lord Jesus Christ, who wouldst be despoiled of Thy garments, and stripped and scourged for my sake; grant me by a sincere and entire confession of my sins to put off the old man, with all his acts, and never to appear devoid of virtue in Thy sight. Amen.”
The ancient Eastern liturgy of St. James has most beautiful “prayers of the veil” which makes reference to the flesh of Our Lord as the veil : “We thank Thee, Lord our God, that thou hast given us the freedom of entry into the holy place by the blood of Jesus, inaugurating for us a new and living way through the veil of His flesh”, and “…unveiling the coverings of the mysteries which in symbol surround this sacred rite, show them to us clearly and fill the eyes of our minds with Thy incomprehensible light, and purifying our poverty from every defilement of flesh and spirit….”
Does the N.O. even make use of chalice veils? Or have they gone the way of Communion rails?
A deacon once told me that chalice coverings (He probably was referring to the pall.) had been used only for the practicality of keeping flies out. While it certainly would do that, there is rich symbolism behind the use of the chalice veil which has been forgotten or ignored. May God in His kindness “show them to us clearly and fill the eyes of our minds with [His] incomprehensible light.”