Chicken pox is a viral disease, so why then has the World Health Organization (WHO) not eliminated chicken pox like smallpox?
Smallpox still exists in labs.
Eliminating a virus from the world is an immensely costly undertaking. As with most things in real life, cost vs. benefit (and feasibility) need to be taken into account. Unfortunately, there is a limited amount of money available to fight disease.
The overall mortality rate of smallpox is about 30%. That's a very high mortality rate, one that shaped history significantly.
By contrast, of a yearly 4 million people who contracted chicken pox (in the US, before the vaccine), only 100 to 150 died each year.
The death rate of smallpox: 30%. The death rate of chicken pox: .00375%
Maybe someday chicken pox will go the way of small pox. But our limited monies need to be devoted to eliminating viruses that cause greater harm, e.g. polio and others.
Also, not all viruses are equally "eliminatable", e.g. H1N1, HIV, etc.
As well as the risk associated with the viruses (as explained in anongoodnurse's answer), chickenpox isn't a good candidate for elimination because of its lifelong carrier state. With smallpox (like polio and measles, which are also candidates for eradication) there is no carrier state, so eliminating the virus at one time point means the virus will not return. With chickenpox, you could eradicate every active case, and next week an adult carrier will start shedding the virus again and start new rounds of infection. There is as yet no way of eliminating the virus from carriers, so it's impossible to eradicate chickenpox or any other virus that enters a similar long-term latent/carrier state, which includes all the herpesviruses, HIV, adenoviruses, etc.