The Flaming Chalice
Unitarians believe in the oneness of God. Like Muslims, Christadelphians, Jehovah's Witnesses and Jews, the Unitarians believe there is no Holy Trinity, since God is indivisible. Their concept of the Trinity is that it 'splits' God into three forms: the Father, the Holy Spirit, and Jesus Christ.
Just as other Christians feel that the Unitarians misunderstand the true nature of the Trinity, the Unitarian symbol itself can easily be mis-interpreted.
Whilst Unitarians do celebrate Communion, the chalice is not necessarily a reminder of the Last Supper. Rather it represents the Father, cradling the world in His arms as a father would cradle a baby. The Holy Spirit is often portrayed as fire or a flame, which we also see in this symbol. And Jesus Christ's representation is obviously the cross, which is the clear outline of the Unitarian symbol.
So why did the Unitarians choose an image that could be interpreted as The Trinity, or at least something that looks like a cross?
The designer of the symbol, Austrian artist Hans Deutsch, created the symbol during the Second World War as the logo for the Unitarian Service Committee (USC), a group that helped Eastern European Jews and Unitarians to escape Nazi persecution. Deutsch envisioned the altar chalice used by Greeks and Romans who would burn oil as a symbol of devotion to the gods. For the Unitarians, it was a symbol of devotion to helping people.
This follows the Christian tradition of helping people, and since Unitarianism stems from Christianity, the similarity to a cross has never been a problem for the Unitarian church.
See also Unitarian Universalism emblem
For other crosses with flames, see Flaming Cross