This Bible contradiction is from the Skeptic's Annotated Bible.
Esther 3:1 View context
After these things did king Ahasuerus promote Haman the son of Hammedatha the Agagite, and advanced him, and set his seat above all the princes that [were] with him.
No, Agag and all Amalekites were killed in a God-ordained genocide.
1 Samuel 15:2-3 View context
Thus saith the LORD of hosts, I remember [that] which Amalek did to Israel, how he laid [wait] for him in the way, when he came up from Egypt.
Now go and smite Amalek, and utterly destroy all that they have, and spare them not; but slay both man and woman, infant and suckling, ox and sheep, camel and ass.