Apex domains cannot have CNAME records.
Question and response
Question
dig uchicago.edu. NS
Answer
uchicago.edu. 3 NS ucns4.uchicago.edu.
uchicago.edu. 3 NS ucns1.uchicago.yale.edu.
uchicago.edu. 3 NS ucns1.uchicago.uiowa.edu.
uchicago.edu. 3 NS ucns3.uchicago.edu.
Authority
The response has no authority records.
Additional
ucns3.uchicago.edu. 3 A 128.135.249.250
ucns4.uchicago.edu. 3 A 128.135.247.250
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0