The single-celled organism that lacks a nucleus is called a prokaryote.

Here's why:

* Prokaryotes are a domain of life that includes bacteria and archaea. They are simple cells that lack a membrane-bound nucleus and other membrane-bound organelles.

* Eukaryotes, the other major domain of life, include plants, animals, fungi, and protists. They have complex cells with a nucleus and other membrane-bound organelles.

So, while many single-celled organisms exist, the defining characteristic of a prokaryote is the lack of a nucleus.