I don't know how to ask him/her without sounding overconfident... (i.e. How dare a little noobie even talk to the CEO?)
At the end of day - your CEO is just a person. Ask and see what happens. I bet you "little noobies" don't ask him out to lunch very much, so he might like that in you, and maybe even say yes. "You miss 100% of the shots you don't take". Go for it!
Yes, thank you for the boost!