**Core Concept**
The first investigation for a breast lump in a young woman involves assessing the risk of breast cancer, which is influenced by factors such as age, family history, and genetic predisposition. A thorough clinical examination and imaging studies are essential to differentiate between benign and malignant lesions.

**Why the Correct Answer is Right**
The first step in evaluating a breast lump is to perform a thorough clinical examination to assess the size, location, mobility, and consistency of the lump. This is followed by imaging studies such as ultrasonography or mammography to provide additional information about the nature of the lump. In a 26-year-old woman, the likelihood of breast cancer is relatively low, but it is essential to investigate further to rule out any potential malignancy.

**Why Each Wrong Option is Incorrect**
**Option A:** Mammography alone is not sufficient as the first investigation, especially in young women with dense breast tissue, as it may not provide an accurate diagnosis.
**Option B:** Fine-needle aspiration cytology (FNAC) may be performed later in the diagnostic process, but it is not the first investigation, as it requires a clinical and imaging diagnosis before proceeding with a biopsy.
**Option C:** A biopsy may be necessary in some cases, but it is not the first investigation, as it requires a thorough clinical and imaging evaluation before proceeding with tissue sampling.
**Option D:** A chest X-ray is not directly relevant to the evaluation of a breast lump and would not be the first investigation.

**Clinical Pearl / High-Yield Fact**
In young women with breast lumps, it is essential to consider the possibility of benign conditions such as fibroadenoma, which are common in this age group.

**Correct Answer:** A. Clinical examination and imaging studies such as ultrasonography or mammography.