Chicken pox is only serious for pregnant women that haven't had chicken pox before or people with serious auto immune conditions such as HIV (when it's live), aids or are having chemotherapy or radiotherapy and haven't had it before. It will be more severe when adults catch it, even healthy ones but not deadly or serious, just worse than what a child experiences.
Babies born to mothers that have had chicken pox before will be immune in the first months of life due to the mother passing on anti bodies. From then, it's fine for a baby to catch it. It's recommended that people who are around immune compromised people and haven't had chicken pox before are vaccinated to prevent the immune compromised person getting the infection. This is because the person with chicken pox is contagious before the spots appear so it's hard to tell when someone has it until the spots appear.
It's highly recommend to let your healthy child catch it so they are immune and will only experience mild illness from getting it.
I think people on here haven't got their facts right. It is not deadly or serious for pregnant women and their unborn babies, only some, a small amount where the woman has never had chicken pox. 9 out of 10 people contract chicken pox as children. Also, it's not deadly or serious to all immune compromised people as most will have had it as children. It's only dangerous to the one's that have never had it before.
So in theory, it's best to let your child catch chicken pox and they'll have immunity for life. Some people aren't quite immune from catching it and will catch it again but this is very rare. Nurses and doctors that work on wards treating cancer patients and other people with serious immune compromising conditions that haven't had chicken pox before are vaccinated to prevent the patient catching the infection while they are weak and susceptible to complications from the virus. A child with cancer for example that has siblings that haven't had chicken pox before will get vaccinated to protect the child with the weakened immune system. Again, it's only deadly or serious to people with SERIOUS immune system problems while they are at their worst or receiving treatment. These are usually people that are in hospital or requiring hospital treatment. You aren't going to get someone in the category of seriously immune compromised walking about the street or at theme parks while it's likely the infection could kill them because well, they are seriously ill and having hospital treatment. It's still best to keep your child at home while they have open sores to prevent the small chance that they come into contact with a pregnant woman that hasn't had it before or someone with a serious illness that hasn't had it before either