Chickenpox is caused by the varicella-zoster virus (VZV), which is specific to humans. While some animals can contract similar viruses that cause pox-like symptoms, these are different viruses and are not contagious to humans.
It's important to remember that if your pet is showing signs of illness, it's best to consult your veterinarian. They can help diagnose any potential issues and provide the best course of treatment.