How can I gzip standard in to a file and also print standard in to standard out?

I want to execute a command, have the output of that command get gzip'd on the fly, and also echo/tee out the output of that command.

i.e., something like:

echo "hey hey, we're the monkees" | gzip --stdout > my_log.gz

Except when the line executes, I want to see this on standard out:

hey hey, we're the monkees