Step 1: Recall what causes each disease.
Diseases can be caused by different types of pathogens such as bacteria, viruses, fungi, or protozoa. Knowing which pathogen causes a disease helps decide the type of treatment needed.
Step 2: Identify the cause of cholera.
Cholera is caused by a bacterium called Vibrio cholerae. It spreads through water or food contaminated with this bacterium and leads to severe watery diarrhea and dehydration. Since it is caused by a bacterium, it can be treated with antibiotics along with fluid replacement.
Step 3: Confirm the other diseases are viral.
Chickenpox is caused by the varicella zoster virus and spreads easily through the air or contact with fluid from the rash. Hepatitis, especially the common types like hepatitis A and hepatitis B, is caused by hepatitis viruses that attack the liver. Measles is caused by the measles virus, which spreads through respiratory droplets and causes fever along with a characteristic skin rash. All three of these are genuinely viral diseases.
Step 4: Final answer.
Since cholera is caused by a bacterium and not a virus, it is the disease that does not belong with the other three.
\[ \boxed{\text{Cholera}} \]