I haven't read any of the other replies, but here is my experience.
I had the chicken pox and some measles. My brother had the chicken pox and some measles.
My kids...they both have had the MMR because they go to public school. Neither had the chicken pox vaccine. It was, at that time, not required and I didn't want them to have the vaccine anyway.
About 4 years ago, there was a big outbreak of chicken pox in the gradeschool, and even the kids who were vaxed for chicken pox GOT the chicken pox and spread the chicken pox.
So...I take ds#2 to the doctor to confirm he has chicken pox. The doc says good deal, your kid has chicken pox, now he will have life-long immunity. He said he did NOT want his kid to get the chicken pox vaccine, but his wife insisted on it. He said they still don't know how long the vaccine will work AND that vaccinated kids are still getting and spreading the chicken pox.
However, if your child has immune system problems, that changes everything maybe. I don't know for sure, since both my kids have healthy immune systems so far.
Oh, and ds#1...he has had some mystery rashes, may have been chicken pox, don't know....doctor in those towns didn't know cuz I am guessing none of them have SEEN chicken pox.
When ds#2 got the chicken pox, ds#1 did not get it, so I am guessing he has had it before and it was a very mild case and we just didn't know he had it.

When ds#2 got the chicken pox about 4 years ago and lots of his classmates who were vaccinated got the chicken pox, there was no push to vaccinate the kids.
Now, however, we just recently got a note that said it is a requirement from the state to have your children vaccinated against chicken pox if they are in public school, unless your kid has already HAD the chicken pox and I had to give them a date he had them...
I wrote a little note at the bottem that during the 4th grade chicken pox breakout that most of the kids who GOT chicken pox and were spreading it around HAD been vaccinated, so not so sure the vaccine is doing that much good.
But what do I know.