GZip/Deflate on PCL clients
Support http compression on clients (Xamarin/sl5) with Microsoft Compression BCL library

Should be possible with the new HttpClient-based JsonHttpClient released in v4.0.42: https://github.com/ServiceStack/ServiceStack/wiki/C%23-client#jsonhttpclient
This MSDN Article shows how to enable it using a custom HttpClientHandler: http://blogs.msdn.com/b/dotnet/archive/2013/06/06/portable-compression-and-httpclient-working-together.aspx
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Drazen Dotlic commented
This is actually not going to work for us since we use Silverlight (gasp!) on the client, but it's not a big deal, we already have something in place to help us with decompression (the smallest thing that should work should be Zlib.Portable from here: https://github.com/advancedrei/Zlib.Portable)
FYI, we've been using HttpClient for 2 years now ;)