Final answer:
The organism with the described characteristics is a member of the domain Archaea, a type of prokaryote that lives in extreme environments and lacks a nucleus.
Step-by-step explanation:
The organism you described is unicellular, lacks a nucleus, utilizes chemosynthesis, and lives in extreme environments. Based on these characteristics, the organism in question is most appropriately categorized as a member of the domain Archaea. These are types of prokaryotes, which are unicellular organisms that do not have a nucleus or other membrane-bound organelles. Archaea are known for inhabiting extreme environments and are distinct from Bacteria and Eukarya, the other two domains of life. Although Archaea share some traits with bacteria, such as being prokaryotic, they are genetically and biochemically unique. They are not eukaryotic, so they do not belong to the domain Eukarya, which includes organisms with a nucleus, like animals, plants, and fungi. Therefore, the correct answer to the question is C. Archaea.