How can I convert a string into a GZIP Base64 string?

I've been trying to figure out using GZIPOutputStream's and the like but have had no success with understanding them. All I want to do is convert a string of characters - "A string of characters" into a GZIP Base64 format. How can I do this?

By GZIP Base64 format, I mean the string is first compressed using GZIP, then converted into Base64.