What percentage of people are naturally immune to the chicken pox virus?
If a newborn baby’s mother has had chickenpox, some of her antibodies to the varicella virus (which causes chickenpox) will pass to the baby.
However, this is only passive immunity, as the baby is getting antibodies without having made its own. This only lasts a few weeks or months, after which time the infant will be vulnerable again. Source: NHS site on chickenpox.
Another example of this passive immunity is when we use varicella zoster immunoglobulin to prevent chickenpox in vulnerable people (e.g. immunosuppression or during pregnancy) if they have been exposed to chickenpox but are know to not be immune themselves (immunity can be determined from a blood test looking for varicella IgG antibodies). In this situation, standard vaccination (which stimulates the immune system to produce its own antibodies (and, importantly, to remember this longer term) would not act quickly enough.
I cannot find any data about people who carry immunity from birth into adult life, and it is likely that this is not possible in general. Some people may have avoided significant exposure to chickenpox for their entire life, but it is more likely that they have been exposed and developed immunity but without any symptoms (known as subclinical infection).