Step 1: Understand the leak. In chyluria, fat-laden lymph escapes into the urinary tract and turns the urine milky. The aim of diet therapy is to keep fat out of the lymphatic channels so the leaking fluid is no longer milky.
Step 2: The route of fat absorption decides this. Dietary long chain fats are re-esterified, wrapped into chylomicrons, and enter the lacteals and then the lymphatic system, which is exactly the pathway that feeds the chyle leak.
Step 3: Medium chain fatty acids avoid that pathway. Being more water soluble, they are absorbed straight into the portal blood and go to the liver, skipping the lymphatics. Switching the patient to a medium chain triglyceride diet starves the lymph of fat and clears the chyluria.
Step 4: Therefore the correct dietary choice is medium chain fatty acids.
\[\boxed{\text{Medium chain fatty acids}}\]