Nucleus:
The nucleus is a membrane-bound organelle that contains the genetic material of the cell. It is responsible for regulating gene expression and controlling the activities of the cell. The nucleus contains nucleic acids in the form of DNA and RNA.

Nucleolus:
The nucleolus is a substructure within the nucleus. It is involved in the production of ribosomes, which are responsible for protein synthesis. The nucleolus contains nucleic acids in the form of DNA and RNA.

Chloroplast:
Chloroplasts are organelles found in plant cells and some algae. They are responsible for photosynthesis, the process by which light energy is converted into chemical energy. Chloroplasts contain nucleic acids in the form of DNA and RNA.

Ribosome:
Ribosomes are small organelles involved in protein synthesis. They are composed of ribosomal RNA (rRNA) and proteins. Ribosomes do not have a membrane and are found either free in the cytoplasm or attached to the endoplasmic reticulum. They do not possess their own nucleic acid because they rely on the genetic information encoded in the mRNA (messenger RNA) to synthesize proteins.

Plasma Membrane:
The plasma membrane, also known as the cell membrane, is a lipid bilayer that surrounds the cell. It regulates the movement of substances in and out of the cell and plays a role in cell signaling. While the plasma membrane contains phospholipids and proteins, it does not possess nucleic acids.

Conclusion:
Among the given options, the plasma membrane is the only organelle that does not possess nucleic acids. The nucleus, nucleolus, and chloroplasts all contain nucleic acids in the form of DNA and RNA. Ribosomes, on the other hand, do not possess their own nucleic acid and rely on mRNA for protein synthesis.