Final answer:
The Golgi apparatus is the organelle in a eukaryotic cell that is not surrounded by a double membrane, unlike the mitochondrion, chloroplast, or nucleus.
Therefore, the correct answer is C.
Step-by-step explanation:
The organelle in a eukaryotic cell that is not surrounded by a double membrane is the Golgi apparatus. While mitochondria and chloroplasts have a double membrane structure and the nucleus is also enveloped by a double membrane called the nuclear envelope, the Golgi apparatus does not share this characteristic. Each of these other organelles is either clear evidence of endosymbiotic relationships in the past, as is the case with mitochondria and chloroplasts, or is a central organelle in eukaryotic cells like the nucleus.
It's important to note that chloroplasts and mitochondria are surrounded by double membranes due to their endosymbiotic origins, and the nuclear membrane is distinct from the endomembrane system despite having a double membrane structure.
Therefore, the correct answer is C. Golgi apparatus, which is part of the endomembrane system but does not have a double membrane.