Apex domains cannot have CNAME records.
Question and response
Question
dig chickenkiller.com. NS
Answer
chickenkiller.com. 4 NS ns3.afraid.org.
chickenkiller.com. 4 NS ns1.afraid.org.
chickenkiller.com. 4 NS ns2.afraid.org.
chickenkiller.com. 4 NS ns4.afraid.org.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0