**Core Concept**
Chronic thiazide therapy can lead to persistent hypercalcemia due to its effect on the kidneys, specifically the increased reabsorption of calcium in the distal convoluted tubule.

**Why the Correct Answer is Right**
The mechanism behind this phenomenon involves the increased activity of the sodium-calcium exchanger in the distal convoluted tubule. Thiazides inhibit the sodium-chloride cotransporter, leading to a decrease in sodium reabsorption. As a result, the sodium-calcium exchanger is activated, promoting the reabsorption of calcium ions into the bloodstream. This increased calcium reabsorption contributes to the development of hypercalcemia.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not accurately describe the mechanism of thiazide-induced hypercalcemia.
* **Option B:** This option is incorrect because it suggests that thiazides cause hypercalcemia by increasing calcium absorption in the gut, which is not the case.
* **Option C:** This option is incorrect because it implies that thiazides cause hypocalcemia, which is the opposite of the correct answer.

**Clinical Pearl / High-Yield Fact**
Thiazide-induced hypercalcemia is a common side effect of long-term thiazide therapy, particularly in patients with mild renal insufficiency.

**Correct Answer:** C.