CloudFront with S3 website as origin is not servin

AWS now supports gzipping files through CloudFront

I've followed along with all of the instructions in Serving Compressed Files, and yet gzipping is not working.

I have an S3 bucket set up as a website that CloudFront is using as the origin.

Compress Objects Automatically is enabled
I am serving files with the correct content types such as application/javascript and text/css
The files are within 1,000 and 10,000,000 bytes
The S3 website serves the files with a Content-Length as far as I know
To be extra sure nothing was cached, I both invalidated the entire S3 bucket and uploaded newer versions of the files to S3.
Additionally, the web browser I am using, Chrome, does accept gzipped files.

Despite all this, I can't get gzipping to work. I have gotten everything else including SSL working perfectly, and you can visit the site here: https://formulagrid.com/

If you open up the chrome console, you'll notice that none of the files being served from S3 are being gzipped. The only gzipped files such as the google font are the ones I'm grabbing from other CDNs.

I hit the same error today and solved it by adding a CORS rule to the S3 bucket. This rule ensures the Content-Length header is sent to Cloudfront so content can be gzipped:

S3 > Bucket > Permissions > CORS Configuration

<?xml version="1.0" encoding="UTF-8"?>
<CORSConfiguration xmlns="http://s3.amazonaws.com/doc/2006-03-01/">
    <CORSRule>
        <AllowedOrigin>*</AllowedOrigin>
        <AllowedMethod>GET</AllowedMethod>
        <MaxAgeSeconds>3000</MaxAgeSeconds>
        <AllowedHeader>Authorization</AllowedHeader>
        <AllowedHeader>Content-Length</AllowedHeader>
    </CORSRule>
</CORSConfiguration>

Credit goes to Robert Ellison: http://ithoughthecamewithyou.com/post/enable-gzip-compression-for-amazon-s3-hosted-website-in-cloudfront

As far I know, this seems to be an undocumented requirement.