Chickenpox Vaccine (varicella)

I'm really torn if I should let my son have this vaccine. Been reading alot online and I really like the pro's to this vaccine but it's also resulted in deaths. One out of every million doses but still. I read a comment to a post about vaccines on here where the mother said both of her kids died after getting the vaccine. This scares me so much to think this vaccine could possibly kill my child. Could it? How? My son doesn't have any immune deficiencies or congenital problems so is it safe for him? Will my pediatrician be able to tell me? He'll be a year in a few months so I've really been thinking about this. I know it's required for school too in my State. Ugh anyone have any good info about my concern? UPDATE: Hi thank you everyone that answered with helpful information and advice. I'd also like to know your views on getting the varicella vaccine within 28 days of the MMR vaccine. Is it better to get them together or spaced apart after 28 days?? I've read different things about this and am just wondering. Thanks!!