"a brim-full living chalice"
Christ with the Eucharist
In the Christian tradition, the cup Jesus used at the Last Supper
is known as the Holy Chalice. 'Then he took the cup, gave thanks and offered it to them, saying, "Drink from it, all of you. This is my blood of the covenant, which is poured out for many for the forgiveness of sins. I tell you, I will not drink of this fruit of the vine from now on until that day when I drink it anew with you in my Father's kingdom"' (Matthew 26:27-29
Some Christians believe the original chalice, which they call the Holy Grail, was used to collect Jesus' blood after the crucifixion. Other Christians believe the apostle Peter took the cup with him to Rome after Jesus used it at the Last Supper. Most people, Catholics in particular, simply believe the wine consecrated in mass becomes the figurative 'blood of Christ' and so all church chalices are considered sacred.
The Bible itself does not suggest Jesus' cup was of any significance.