**Core Concept**
Hyper IgE syndrome (HIES) is a rare genetic disorder characterized by recurrent cutaneous and pulmonary infections, eczema, and elevated levels of IgE antibodies. The condition results from mutations in the STAT3 or TYK2 genes, leading to impaired T-cell function and an overactive Th2 response.

**Why the Correct Answer is Right**
The characteristic chest X-ray finding in HIES is the presence of pulmonary infiltrates, often described as fleeting or migratory. These infiltrates are thought to result from the accumulation of eosinophils and neutrophils in the lungs, secondary to the Th2-driven inflammation. The pathophysiology of HIES involves impaired T-cell function, particularly in the Th1 subset, which normally helps to regulate the immune response and prevent excessive inflammation.

**Why Each Wrong Option is Incorrect**
**Option A:** Wiskott-Aldrich syndrome is a syndrome characterized by eczema, thrombocytopenia, and recurrent infections, but it is not typically associated with the specific chest X-ray findings seen in HIES.

**Option B:** Di George syndrome is a disorder characterized by thymic aplasia or hypoplasia, leading to impaired T-cell development and function. While it can result in recurrent infections, the chest X-ray findings in Di George syndrome are typically different from those seen in HIES.

**Option D:** Chediak Higashi syndrome is a rare disorder characterized by oculocutaneous albinism, bleeding tendency, and recurrent infections. The chest X-ray findings in Chediak Higashi syndrome are not typically described as fleeting or migratory pulmonary infiltrates.

**Clinical Pearl / High-Yield Fact**
In HIES, the skin manifestations often precede the pulmonary findings, and the presence of eczema and elevated IgE levels should raise suspicion for this diagnosis. Remember the classic triad of HIES: eczema, elevated IgE, and recurrent skin and pulmonary infections.

**✓ Correct Answer: C. Hyper IgE syndrome**