**Core Concept**
Chloroma, also known as granulocytic sarcoma, is a rare extramedullary tumor composed of immature granulocytes. It is often associated with acute myeloid leukemia (AML) and can manifest as a painless proptosis. The diagnosis of chloroma requires a combination of clinical evaluation and specific laboratory tests.

**Why the Correct Answer is Right**
The next investigation to diagnose chloroma as the cause of painless proptosis would be a bone marrow biopsy. This is because chloroma is a tumor composed of immature granulocytes, which can be identified in the bone marrow. A bone marrow biopsy would provide a definitive diagnosis by demonstrating the presence of these immature cells. Additionally, a bone marrow biopsy can also assess the involvement of the bone marrow by AML, which is often associated with chloroma. The presence of leukemic blasts in the bone marrow would support the diagnosis of AML and chloroma.

**Why Each Wrong Option is Incorrect**
**Option A:** Imaging studies such as CT or MRI would not be sufficient to diagnose chloroma as they may not be able to distinguish it from other orbital tumors. While imaging studies can help identify the presence of a mass, they do not provide a definitive diagnosis.

**Option B:** A complete blood count (CBC) may show anemia, thrombocytopenia, and leukopenia, but it would not provide a definitive diagnosis of chloroma. A CBC can help identify the presence of leukemia, but it would not confirm the presence of chloroma.

**Option C:** A biopsy of the orbital mass would be useful in diagnosing chloroma, but it is not the next investigation. A bone marrow biopsy is a more specific test that can diagnose both chloroma and AML.

**Option D:** Serum lactate dehydrogenase (LDH) levels may be elevated in chloroma, but it is not a specific marker for this condition. Elevated LDH levels can be seen in various conditions, and a bone marrow biopsy would be required to confirm the diagnosis.

**Clinical Pearl / High-Yield Fact**
Chloroma is a rare extramedullary tumor that can manifest as a painless proptosis. It is often associated with acute myeloid leukemia (AML), and a bone marrow biopsy is essential in diagnosing both conditions.

**Correct Answer:** C. A bone marrow biopsy.