Is it possible to compress a very large file (~30 GB) using gzip?

AFAIK there is no limit of size for gzip - at least not 30GB. Of course, you need the space for the zipped file on your disc, both versions will be there simultanously while compressing.

bzip2 compresses files (not only big ones :-) better, but it is (sometimes a lot) slower.

if you need a good compresion rate, you can try lzma. it is faster and more efficient than bzip2 and may be faster even than gzip (i don't know that for sure)

http://www.thegeekstuff.com/2010/06/lzma-better-compression-than-bzip2-on-unix-linux/

If you are running into the limit, rearrange. Instead of:

gzip file

do:

gzip < file > file.gz

Works just fine.