Which of the following is a feature of Multiple Endocrine Neoplasia type I (MEN I)?

The correct feature of Multiple Endocrine Neoplasia type I (MEN I) is acromegaly, which is primarily associated with the overproduction of growth hormone, often due to a pituitary adenoma. MEN I, also known as Wermer's syndrome, involves a triad of conditions: pituitary tumors (often secreting growth hormone), hyperparathyroidism, and pancreatic endocrine tumors. The presence of acromegaly indicates a functioning pituitary tumor, which is a common manifestation in patients with MEN I.

The other possibilities do not align with the characteristics of MEN I. Pheochromocytoma is typically found in Multiple Endocrine Neoplasia type II (MEN II), while hyperthyroidism and medullary thyroid cancer are also more associated with MEN II. In MEN I, the distinctive feature of acromegaly due to growth hormone-secreting tumors is more specific, highlighting its significant role in the syndrome's presentation.