Final answer:
The hippocampus is the part of the brain that is involved in memory and atrophies in response to chronic stress.
Step-by-step explanation:
The part of the brain involved in memory that atrophies in response to chronic stress is the hippocampus. The hippocampus is associated with declarative and episodic memory as well as recognition memory. Stress can have a significant impact on the hippocampus, leading to its shrinkage (atrophy). On the other hand, the amygdala is involved in fear and the emotional component of memory, but it is not the main part affected by chronic stress in terms of atrophy related to memory retention. The cerebellum helps with processing procedural memories and is not primarily linked with the impact of stress on memory atrophy. Lastly, the hypothalamus largely regulates autonomic and endocrine functions but is not directly related to memory atrophy due to stress.