From askdrsears.com:

If my child is vaccinated against chickenpox, can he pass the disease on to other people?

Possibly, but it is very rare. Studies show that after fourteen million doses of VV, only three cases have been reported in which the vaccinated person transmitted chickenpox to another person, and those occurred only if the immunized person developed a rash.

And technically the documentation says to keep away from people with compromised immunity, that is, the very sick and young babies (so no visiting A+S to hold the new bub). So most people should be fine.

Ain't medicine fun?

I've just been immunized against Chickenpox (having never had it as a child). The documentation (as well as saying words similar to "well, actually, you know, this might not work...") says I should avoid contact with people who haven't had it for six weeks while the immunized not-so-bad version works it's way through me. I know of a few people to avoid. I suppose if you're scared of me let me know.