"I could have eaten the whole chicken."
Translation:θα μπορούσα να είχα φάει όλο το κοτόπουλο.
Both versions seem familiar to me so you're not the only one who thinks το ολόκληρο κοτόπουλο could be correct!
Based on my gut feeling, I'd say that ολόκληρο το κοτόπουλο is "all the chicken" (emphasising that you finished eating it) and το ολόκληρο κοτόπουλο "the entire chicken, the whole chicken" (emphasising that it was a complete, undivided chicken).
I really find it very weird. Ένα ολοκληρο κοτόπουλο is right, but with the definite article it sounds very wrong. I get that you mean that you can use ολόκληρος in a sentence like we say ο όμορφος άντρας πήγε..=The handsome man went..., but saying η ολόκληρη σοκολάτα έλιωσε is not like saying "the whole chocolate melt" but something like "the chocolate that is whole melt" which has no real meaning.