The story
From poisoned + chalice (“a large drinking cup”), referring to a chalice containing a poisoned drink which is offered to someone. The earliest use of the term cited in the Oxford English Dictionary is in Shakespeare’s Macbeth (c. 1606), in a speech in which Macbeth flinches from the prospective murder of King Duncan: see the quotation.
Etymology from Wiktionary, CC BY-SA 4.0.