The chalice symbolizes the centrality of the Lord's Supper to Disciples life. The St. Andrew's Cross, the national cross of Scotland, focuses attention on the Scotch Presbyterian roots of the church. Thomas and Alexander Campbell both studied in Scotland and were Presbyterians. St. Andrew has been identified with the laity and evangelism, prominent emphases of the Disciples over the years.
The red color of the chalice signifies vitality, spirit and sacrifice.
The chalice and St. Andrew's Cross, symbol of the Christian Church (Disciples of Christ), adopted by the church's General Asssembly in 1971, is a trademark registered with the United States Patent Office."
There are various versions of the chalice as you can see in this background.The most commonly accepted graphic of the chalice is this one on the right.