Is there an easy way to see amount of compression in Chrome?
Updated answer for 2017: Yes.
The size column in the Network tab in Chrome Developer Tools has both the compressed and uncompressed size, for gzip, brotli and whatever comes in future. Eg:
Here the compressed size is 242 KB, the uncompressed size is 1.1 MB
To see both, ensure you have Devtools showing large request rows. You can find the checkbox by the gear icon "Network settings" in the Networks-specific toolbar.
By far the easiest method is to use an online tool. GIDZipTest shows you plenty of detail: the original size, compressed size and compression percentage.
However, it is possible in Chrome with a bit of effort. (Updated for latest Chrome, Sept 2011.)
In the Developer Tools, go to the "Network" tab and reload the page. You will see a list of all the files fetched on the left column. Click the appropriate page/file on the left then the "Headers" tab on the right pane.
Under "Response Headers" you should see "Content-Encoding: gzip" followed by a "Content-Length" header. This is the size of the compressed content.
Finding the uncompressed size is more difficult. If you're serving up static files you can simply check its size. For dynamic content you'll have to copy-paste the HTML into a text editor and save it to check the exact size.
Update for 2017
When using large icons, the chrome dev tools show a before and after compression size in the network tabs.
I confirmed by switching gzip off and on on my webserver.
