I've found myself (often in IRC) copying a URL from the scrollback buffer into the paste buffer, putting it on the system clipboard, and pasting the URL into Chrome.
bind \ run "open \"`tmux show-buffer`\""
This binding sends the contents of the paste buffer to the
open command, which will open your default web browser for
https URLs. If you have an application set up to handle other URL schemes, those will work too.