Unfortunately, I failed to solve this issue, but I got around it.
Initially I downloaded RSSOwl for Linux (64 Bit) from here: http://www.rssowl.org/download. However, I would start to get the error message:
Error Creating Browser: RSSOwl was unable to create a browser for reading news. Please refer to the FAQ for further help. Click 'Ok' to open the FAQ now..
This issue is described in RSSOwl’s FAQ (http://www.rssowl.org/help#item_6j). However, following those instructions did not resolve my problem. Ultimately I downloaed the Ubuntu 64-bit Debian package from here: http://www.ubuntuupdates.org/package/getdeb_apps/precise/apps/getdeb/rssowl. Executing that installation of RSSOwl did have this problem.