In some people, however, the immune system does not generate these antibodies that remember the virus. This can happen in people who are very young when they get chickenpox (less than six months old), or who have some disorder of their immune system.
Since you had chickenpox at such a young age, there is a possibility that you never developed good antibodies to it, although it may be that you did. The only way to know is to get a blood test that measures how much antibody you have to the chickenpox virus. If you have a high enough level of the antibody, there is no need to get the vaccine, as you are already protected. If your antibody level (or titer) is low, then you should get the vaccine, as chickenpox is a much more serious illness in adults than in children, and we know that the vaccine works very well to prevent it.