**Core Concept**
The extraperitoneal approach to left sympathectomy involves dissecting through the retroperitoneal space to access the sympathetic chain, which runs along the vertebral bodies in the thoracic and lumbar regions. This procedure requires careful manipulation to avoid injuring nearby structures.

**Why the Correct Answer is Right**
In the extraperitoneal approach to left sympathectomy, the left renal vein is at risk of injury. This is because the left renal vein crosses over the left sympathetic chain, and dissection in this area can compromise its integrity. The left renal vein is a critical structure that carries blood from the left kidney to the inferior vena cava. Injury to this vein can lead to severe bleeding and potentially life-threatening complications.

**Why Each Wrong Option is Incorrect**
**Option A:** The left gonadal vein is not typically at risk in an extraperitoneal approach to left sympathectomy. While it is located in the retroperitoneum, it is not as closely associated with the sympathetic chain as the left renal vein.

**Option B:** The left adrenal gland is not typically at risk in an extraperitoneal approach to left sympathectomy. While it is located in the retroperitoneum, it is not as closely associated with the sympathetic chain as the left renal vein.

**Option C:** The left testicular vein is not typically at risk in an extraperitoneal approach to left sympathectomy. While it is located in the retroperitoneum, it is not as closely associated with the sympathetic chain as the left renal vein.

**Clinical Pearl / High-Yield Fact**
In retroperitoneal surgery, careful identification and preservation of the left renal vein is crucial to avoid complications.

**Correct Answer:** D. The left renal vein.