## **Core Concept**
The chief extensor of the thigh at the hip joint is the **gluteus maximus muscle**. This muscle plays a crucial role in movements such as walking, running, and climbing stairs. The primary nerve responsible for innervating the gluteus maximus is the **inferior gluteal nerve**.

## **Why the Correct Answer is Right**
The **gluteus maximus** is the largest muscle in the buttock region and is primarily responsible for hip extension and external rotation. It is innervated by the **inferior gluteal nerve (L5, S1, S2)**, which arises from the sacral plexus. This nerve supply is essential for the muscle's function in extending the thigh at the hip joint.

## **Why Each Wrong Option is Incorrect**
- **Option A:** The **superior gluteal nerve** primarily innervates the gluteus medius, gluteus minimus, and tensor fasciae latae muscles, which are involved in hip abduction and internal rotation, not extension.
- **Option B:** The **femoral nerve** primarily supplies the muscles of the anterior thigh compartment, including the quadriceps femoris, which is involved in knee extension, not hip extension.
- **Option C:** The **tibial nerve** primarily supplies the muscles of the posterior thigh and leg, which are involved in knee flexion and ankle movements, not hip extension.

## **Clinical Pearl / High-Yield Fact**
A key clinical correlation to remember is that weakness of the gluteus maximus muscle can lead to **Trendelenburg's sign** or **positive Trendelenburg test**, indicating hip abductor weakness. However, specifically for the gluteus maximus, a useful fact is that it is the primary extensor of the hip joint and is crucial for maintaining an upright posture.

## **Correct Answer:** D. Inferior Gluteal Nerve.