If one person has chickenpox once, there is no chance of suffering from it again. This happens because when the immune system first sees an infectious microbe, it responds against it and them remembers it specifically. So the next time that particular microbe, or its close relatives enter the body, the immune system responds with even greater vigour. This eliminates the infection even more quickly than the first time around. This is the basis of the principle of immunization. Immunisation saves person from diseases.